Formulas: Frequency, Wavelength and E photon (Bohr Model Formula)

E photon formula when given frequency (v)

E photon = h X v

E photon formula when given wavelength (λ)

E = h X c / λ

h =

6.626 × 10^-34 J x S (Planck’s Constant). This constant describes the size of the smallest “packets” of energy in the universe. It is the link between the frequency of a wave and the energy of a particle.

c =

3.0 × 10⁸ m/s. The speed of light; acts as the bridge between wavelength and frequency. It is how fast energy moves forward through space. It never changes.

To find Wavelength (λ)

(λ) = c/v (wavelength MUST be in meters). Distance of one peak point to another, it’s how long one wave is.

To find Frequency (v)

v = c/λ The speed of the vibration. It is how often the wave “vibrates or wiggles” every second”.

Bohr Model Formula

When an electron jumps between n levels (orbitals), it either absorbs or releases a photon. To find that energy, we use the Bohr Model formula (see image):

• E: The energy of the photon emitted or absorbed.

• R_H (Rydberg Constant): This is the energy scale for the hydrogen atom. Value: 2.18 × 10^-18 J

• n_final: The ending orbital level

• n_initial: The starting orbital level

If E is positive: the electron absorbed energy (it moved from a low level to a higher level)

If E is negative: the electron released energy (it fell from a higher level to a lower level) and a photon was emitted.

Rydberg Constant (R)

the fundamental unit of energy for atomic transitions.

For energy, the constant is: 2.18 × 10^-18 Joules. This represents the energy needed to completely pull an electron away from a Hydrogen atom (ionization).

For wavelength, the constant is 1.097 × 10⁷ m^-1. This number is used to calculate the physical size of the light wave emitted.