Actividades resueltas modelos atómicos

Introduction

• This document contains solved exercises on atomic structure for 1st year of Bachillerato by Professor A. Zaragoza López.

• It offers a theoretical approach in Chemistry that mirrors the methodical steps in Physics.

Exercise Resolved No. 1

Problem Statement

• A laser emits radiation with a wavelength of 7800 Å.

Tasks

a) Calculate the frequency of this radiation. b) Calculate the energy of a photon of the same frequency.

Given Data

• 1 Å = 10^-10 m

• Speed of light (c) = 3 x 10^8 m/s

• Planck's constant (h) = 6.63 x 10^-34 J.s

Resolution

a) Frequency Calculation:

• Wavelength = 7800 x 10^-10 m

• Frequency (v) = c / wavelength = 3 x 10^8 m/s / (7800 x 10^-10 m) = 3.85 x 10^14 Hz b) Energy Calculation:

• E = h * frequency = (6.63 x 10^-34 J.s) * (3.85 x 10^14 s^-1) = 2.55 x 10^-19 J

Problem Resolved No. 2

Problem Statement

• Calculate the frequency emitted by an electron in the hydrogen atom transitioning from n = 4 to n = 1.

Given Data

• R_H = 2.18 x 10^-18 J

• h = 6.63 x 10^-34 J.s

• c = 3 x 10^8 m/s

Resolution

• Energy for n = 4: E4 = -R_H/n^4 = -2.18 x 10^-18 J / 4^2 = -0.136 x 10^-18 J

• Energy for n = 1: E1 = -R_H/n^1 = -2.18 x 10^-18 J

• Energy difference: E = E4 - E1 = -0.136 x 10^-18 J - (-2.18 x 10^-18 J) = 2.04 x 10^-18 J

• Frequency (v) = E/h = (2.04 x 10^-18 J) / (6.63 x 10^-34 J.s) = 3.07 x 10^15 s^-1

Problem Resolved No. 3

Problem Statement

• Calculate the wavelength emitted by an electron transitioning from n = 5 to n = 2 in hydrogen.

Given Data

• R = 1.096 x 10^7 m^-1

Resolution

• Apply the Rydberg equation: ( \frac{1}{\lambda} = R \left( \frac{1}{n_2^2} - \frac{1}{n_1^2} \right) )

• Calculation: ( \frac{1}{\lambda} = 1.096 x 10^7 m^{-1} \left( \frac{1}{2^2} - \frac{1}{5^2} \right) = 0.230 x 10^7 m^{-1} )

• Resulting in ( \lambda = 1/0.230 x 10^7 m^{-1} = 4.35 x 10^{-8} m)

Problem Resolved No. 4

Problem Statement

• Calculate the energy emitted by a photon during a transition with a wavelength of 100 nm.

Given Data

• h = 6.63 x 10^-34 J.s

• c = 3 x 10^8 m/s

Resolution

• Convert wavelength: 100 nm = 100 x 10^-9 m

• Energy calculation: ( E = \frac{h \cdot c}{\lambda} = \frac{(6.63 x 10^-34 J.s) \cdot (3 x 10^8 m/s)}{100 x 10^{-9} m} = 1.98 x 10^{-18} J)

Problem Proposed No. 5

• Calculate the transition energy when an electron transitions from n = 8 to n = 1 in hydrogen, expressed in electronvolts (eV).

Given Data

• R_H = 2.18 x 10^-18 J

• 1 eV = 1.6 x 10^-19 J

Resolution

• Using the energy levels calculation formula: ( E = E_n (1) \ - E_n (8) ) and convert to eV.

Exercise Resolved No. 6

• An electron transitions among given energy levels.

• Calculate the frequency and wavelength of emitted electromagnetic radiation.

Given Data

• h, 1 eV.

Resolution

• Convert energy from eV to J, then apply E = h*v for frequency calc. and λ = c/v for wavelength calc.

Continue with exercises…

• The remaining exercises follow the same computational methods, demonstrating calculations of frequency, wavelength, and energies related to atomic electronic transitions and radiation emissions.