Comprehensive Chemistry: Significant Figures, Nuclear, and Atomic Structure

What are significant figures?

Significant figures express the precision of a measurement, including all known digits plus one estimated digit.

What does a higher number of significant figures indicate?

It indicates higher precision in the measurement.

What is Rule 1 of significant figures?

Non-zero digits are always significant.

Give an example of a number with 3 significant figures.

72.3 has 3 significant figures.

What is Rule 2 regarding zeros in significant figures?

Zeros between non-zero digits are always significant.

Provide an example of a number with 4 significant figures due to the sandwich rule.

2507 has 4 significant figures.

What is Rule 3 concerning leading zeros?

Leading zeros are not significant as they only position the decimal point.

How many significant figures does 0.0025 have?

It has 2 significant figures.

What is Rule 4 about trailing zeros?

Trailing zeros are significant only if there is a decimal point.

Give an example of a number with 4 significant figures because of a decimal point.

100.0 has 4 significant figures.

What happens to trailing zeros in a number without a decimal point?

They are not significant.

How many significant figures does 89100 have?

It has 3 significant figures.

What is the first step in rounding a number to a specific number of significant figures?

Underline or identify the last significant digit desired.

What should you do if the next digit to the right is 5 or above?

Round the last significant digit up.

How do you apply significant figures in multiplication and division?

The final answer must have the same number of significant figures as the measurement with the fewest sig. figs.

What is the rounding rule for addition and subtraction?

The answer should be rounded to the decimal place of the least precise measurement.

What is the mean in basic statistical measures?

The average of a set of data points, calculated by summing all values and dividing by the number of data points.

Define median in the context of statistical measures.

The middle value when data points are ordered from least to greatest.

What is mode in statistics?

The value(s) that occur most frequently in a dataset.

What does range measure in a dataset?

The difference between the highest and lowest data points.

How is variance defined?

Variance is the average squared deviation of data points from the mean.

What is standard deviation?

A measure that quantifies how much data points vary from the mean.

What is the standard deviation in relation to variance?

The standard deviation is the square root of variance, providing a measure of spread in the original units.

How is probability defined?

Probability measures the likelihood of an event occurring, expressed as a number between 0 (impossible) and 1 (certain).

What distinguishes independent events from dependent events?

Independent events: The outcome of one does not affect the other. Dependent events: The outcome of one influences the probability of the other.

What are discrete variables?

Discrete variables take specific, separate values (e.g., number of students).

What are continuous variables?

Continuous variables can take any value within an interval (e.g., height, time).

What does the binomial distribution model?

The binomial distribution models the probability of achieving a fixed number of successes in a fixed number of independent trials, each with the same probability of success.

What parameters define a binomial distribution?

Parameters include n (number of trials) and p (probability of success per trial).

What characterizes a normal distribution?

A normal distribution is symmetric and bell-shaped, characterized by its mean and standard deviation.

What is the significance of the Central Limit Theorem?

The Central Limit Theorem is central to many statistical analyses and states that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases.

What percentage of data falls within one standard deviation of the mean in a normal distribution?

Approximately 68% of data falls within one standard deviation of the mean, 95% within two, and 99.7% within three.

What is sampling in statistics?

Sampling involves selecting a subset from a population to make inferences about the whole.

What is a sampling distribution?

A sampling distribution is the probability distribution of a statistic (e.g., mean) over many samples, which helps estimate the variability of that statistic.

What is estimation in statistics?

Estimation uses sample data to infer population parameters.

What are confidence intervals?

Confidence intervals are ranges within which the true parameter is likely to fall, with a specified confidence level (e.g., 95%).

What are alpha (α) particles?

Alpha particles are helium nuclei (2 protons, 2 neutrons) with a charge of +2, stopped by paper or skin.

What are beta (β-) particles?

Beta particles are electrons emitted during decay with a charge of -1, stopped by lead or aluminum.

What are positrons (β+)?

Positrons are positively charged electrons with a charge of +1, also stopped by dense materials like lead.

What are gamma (γ) rays?

Gamma rays are high-energy photons with no charge, very penetrating and stopped by concrete or thick shielding.

What happens during alpha emission?

The nucleus emits an alpha particle, decreasing atomic number by 2 and mass number by 4.

What occurs during beta emission?

A neutron converts into a proton, emitting a beta particle, which increases atomic number by 1 while mass number remains unchanged.

What is the half-life concept?

The half-life (t₁/₂) is the time required for half of the radioactive atoms in a sample to decay; a shorter half-life indicates less stability.

How is the remaining mass after a certain number of half-lives calculated?

Remaining mass = initial mass × (1/2)ⁿ, where n is the number of half-lives elapsed.

What formula is used to solve for the unknown in half-life problems?

Final amount = Initial amount × (1/2)^(time / half-life)

What defines the element of an atom?

The atomic number (Z)

What are cations and how do they differ from anions?

Cations are positively charged particles that lose electrons, typically metals, while anions are negatively charged particles that gain electrons, typically nonmetals.

What are isotopes?

Atoms of the same element with different neutron counts, resulting in different masses but identical chemical properties.

What are the charges and masses of protons, neutrons, and electrons?

Protons: +1 charge, 1 amu mass; Neutrons: 0 charge, 1 amu mass; Electrons: -1 charge, negligible mass (~0.0005 amu).

Where are protons, neutrons, and electrons located in an atom?

Protons and neutrons are located in the nucleus, while electrons are located in the electron cloud.

How do you count subatomic particles in neutral atoms?

Number of protons = atomic number; Number of electrons = atomic number; Number of neutrons = mass number − atomic number.

What are the naming conventions for cations and anions?

Cations are named by the element + 'ion' (e.g., sodium ion); Anions are named by the element + '-ide' (e.g., chloride).

How do isotopes differ in terms of neutron number?

Isotopes differ in neutron number, which affects their mass number.

Provide an example of isotopes and their neutron counts.

Carbon-12 has 6 protons and 6 neutrons; Carbon-14 has 6 protons and 8 neutrons.

What is average atomic mass?

The weighted average mass of an element's isotopes, calculated based on their relative natural abundance and individual isotope masses.

How is average atomic mass calculated using Lithium isotopes?

Average atomic mass = (0.0742 × 6.015) + (0.9258 × 7.015) ≈ 6.94 amu.

What is Rule 2 of significant figures?

Zeros between non-zero digits are significant (Sandwich Rule).

What is Rule 3 of significant figures?

Leading zeros are not significant.

How many significant figures are in the number 72.3?

3 significant figures.

How many significant figures are in the number 699.52?

5 significant figures.

How many significant figures are in the number 2507?

4 significant figures.

How many significant figures are in the number 60.5?

3 significant figures.

What does the number of significant figures indicate?

The precision of the measurement, with more significant figures indicating higher precision.

What are leading zeros in a number, and are they significant?

Leading zeros are the zeros that occur at the beginning of a number before any non-zero digit. They are not significant as they only position the decimal point.

How many significant figures are in the number 0.0025?

There are 2 significant figures in 0.0025 (the 2 and 5).

What is the rule for trailing zeros in a number?

Trailing zeros are significant only if the number contains a decimal point.

How many significant figures does the number 100.0 have?

100.0 has 4 significant figures.

How many significant figures does the number 89100 have?

89100 has 3 significant figures.

What is the process for rounding a number to a specific number of significant figures?

Identify the last significant digit desired, look at the next digit to the right, round up if it is 5 or above, and leave it as is if below 5.

How do you determine the number of significant figures in multiplication and division?

The final answer must have the same number of significant figures as the measurement with the fewest significant figures.

What is the rule for rounding in addition and subtraction?

The answer should be rounded to the decimal place of the least precise measurement.

How is the median defined?

The median is the middle value when data points are ordered from least to greatest; if there is an even number of data points, it is the average of the two middle values.

What is the mode in statistics?

The mode is the value(s) that occur most frequently in a dataset.

What is variance?

Variance is the average squared deviation of data points from the mean.

What does probability measure?

Probability measures the likelihood of an event occurring, expressed as a number between 0 (impossible) and 1 (certain).

What are independent events in probability?

Independent events are those where the outcome of one does not affect the outcome of the other.

What are dependent events in probability?

Dependent events are those where the outcome of one influences the probability of the other.

What distinguishes discrete random variables from continuous random variables?

Discrete variables take specific, separate values, while continuous variables can take any value within an interval.

What is a binomial distribution?

A binomial distribution models the probability of achieving a fixed number of successes in a fixed number of independent trials, each with the same probability of success.

What are the parameters of a binomial distribution?

The parameters are n (number of trials) and p (probability of success per trial).

What is the significance of the Central Limit Theorem in statistics?

The Central Limit Theorem states that the distribution of sample means approaches a normal distribution as the sample size increases.

What percentage of data falls within two standard deviations of the mean in a normal distribution?

Approximately 95% of data falls within two standard deviations of the mean.

What percentage of data falls within three standard deviations of the mean in a normal distribution?

Approximately 99.7% of data falls within three standard deviations of the mean.

What occurs during alpha emission?

The nucleus emits an alpha particle, decreasing atomic number by 2 and mass number by 4.

What happens during positron emission?

A proton converts into a neutron, emitting a positron, which decreases atomic number by 1.

What is electron capture?

The nucleus captures an inner orbital electron, converting a proton into a neutron.

What follows other decay types and releases excess energy?

Gamma emission.

Why do nuclides undergo decay?

To achieve a stable neutron-to-proton ratio; instability arises when this ratio deviates from the optimal range.

What is half-life (t₁/₂)?

The time required for half of the radioactive atoms in a sample to decay.

How can you calculate the remaining mass after decay?

Remaining mass = initial mass × (1/2)ⁿ, where n is the number of half-lives elapsed.

How do you solve half-life problems?

Given any three of the four variables—initial amount, final amount, half-life, or total time—you can solve for the unknown using the decay formula: Final amount = Initial amount × (1/2)^(time / half-life).

What defines an atom?

Atoms are neutral particles with equal numbers of protons and electrons, defined by their atomic number (Z).

What are ions?

Charged particles with a different number of electrons than protons; cations (+) lose electrons, while anions (−) gain electrons.

What are the characteristics of protons?

Protons have a charge of +1, a mass of 1 amu, and are located in the nucleus.

What are the characteristics of neutrons?

Neutrons have a charge of 0, a mass of 1 amu, and are located in the nucleus.

What are the characteristics of electrons?

Electrons have a charge of -1, a negligible mass (~0.0005 amu), and are located in the electron cloud.