Question

What wavelength photon is required to excite a hydrogen from the n=1 state to the n=3 state? What is the lowest frequency photon that will be observed?

Answer 1

here ,

for the wavelength

let the wavelength is L

Now, for the transition in HYdrogen

h*c/(wavelength) = -13.6 * e * (1/n1^2 - 1/n2^2)

6.626 *10^-34 * 3 *10^8/(L) = 13.6 * 1.602 * 10^-19 * (1/1^2 - 1/3^2)

solving for L

L = 1.02 *10^-7 m

the wavelength of light used is 1.02 *10^-7 m
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for the lowest frequency photons

h*f = -13.6 * e * (1/n1^2 - 1/n2^2)

6.626 *10^-34 * f = 13.6 * 1.602 * 10^-19 * (1/2^2 - 1/3^2)

f = 4.6 *10^14 Hz

the lowest frequency photon to be observed is 4.6 *10¹⁴ Hz