Which electron transitions will produce a photon of shortest wavelength in the Bohr Hydrogen atom?

Question

a) n = 3 to n = 4
b) n = 4 to n = 1
c) n = 3 to n = 1
d) n = 2 to n = 1

Answer 1

If an electron jumps from a higher orbit to a lower it moves to lower energy level and the energy is emitted as photons. The greater the jump the greater the energy of the photons is. Since the wavelength is proportional to the reciprocal of the energy of the photon, you get the shortest wavelength for the biggest jump. That is case b).


You can analyze it in detail with the following relation for the wavelength of the emissions lines of hydrogen atoms:
1/λ = R·(1/n₁² -1/n₂²)
where
λ is the wavelength
R = 1.097373·10⁷m⁻¹ is the Rydberg constant
n₁ < n₂ are the principal quantum numbers

a) no light emission
b) λ = 97.2·10⁻⁹m
b) λ = 102.5·10⁻⁹m
b) λ = 121.5·10⁻⁹m

Answer 2

Shortest wavelength is greater skill. consequently the utmost skill transition could be the shortest wavelength. answer b) is the main skill, consequently would produce the main skill and shortest wavelength photon.