Frequency in Hz

Question

What would be the frequency (in Hz) of the photon emitted by a He+ ion, if it relaxed from the n = 3 energy state to the n = 2 energy state?

Answer 1

First, we should calculate the wavelength and then convert that to frequency.

1/λ = RZ²(1/n₁² - 1/n₂²)

λ = wavelength

R = Rydberg Constant = 1.097x10⁷m^-1

Z = nuclear charge = 2 for He⁺

n₁ = principal quantum number of the upper level = 3

n₂ = principal quantum number of the lower level = 2

1/λ = (1.097x10⁷m^-1)(2)² (1/4 - 1/9) = 4.388x10⁷m^-1 (0.1389)

1/λ = 6.095x10⁶m^-1

λ = 1.641x10^-7 m

To convert λ to frequency (ν), we can use ν = C/λ where C = speed of light = ~3x10⁸ m/sec

ν = 3x10⁸ ms^-1/1.64x10^-7m = 1.83x10¹⁵ s^-1 = 1.83x10¹⁵ Hz