A hydrogen atom absorb a photon of visible light and it's electron leaves from n=4 and enters n=6 energy calculate the change of energy of the atom and wavelength in (nm) of the photon (R=-2.18×10^-18)

1 answer

To calculate the change in energy of the atom, we can use the formula:

ΔE = E_final - E_initial

Where ΔE is the change in energy, E_final is the final energy level, and E_initial is the initial energy level.

Given that the electron leaves from n = 4 and enters n = 6, we can substitute these values into the formula:

ΔE = (-2.18 × 10^-18) * ((1/n_final^2) - (1/n_initial^2))

ΔE = (-2.18 × 10^-18) * ((1/6^2) - (1/4^2))
ΔE = (-2.18 × 10^-18) * (1/36 - 1/16)
ΔE = (-2.18 × 10^-18) * (16/576 - 36/576)
ΔE = (-2.18 × 10^-18) * (-20/576)
ΔE = 3.817 × 10^-20 J

To calculate the wavelength of the photon, we can use the formula:

ΔE = hc/λ

Where ΔE is the change in energy, h is Planck's constant (6.62607015 × 10^-34 J*s), c is the speed of light (2.998 × 10^8 m/s) and λ is the wavelength.

Substituting the values:

3.817 × 10^-20 = (6.62607015 × 10^-34) * (2.998 × 10^8) / λ

Solving for λ:

λ = (6.62607015 × 10^-34) * (2.998 × 10^8) / (3.817 × 10^-20)
λ = 5.226 × 10^-7 m

Converting this to nanometers:

λ = 5.226 × 10^-7 * 10^9
λ = 522.6 nm

Therefore, the change in energy of the atom is 3.817 × 10^-20 J and the wavelength of the photon is 522.6 nm.