Question

What is the frequency of light released when an electron moves from the 2nd energy level to the 1st
energy level in hydrogen (don't reach for a calculator, you should be able to estimate 3/4s of a
number like 3.3).

Answer 1

The frequency of the light released when an electron moves from the 2nd energy level to the 1st energy level in hydrogen is 2.47 x 10¹⁵ Hz.

The given parameters;

• initial energy level, n₂ = 2
• final energy level, n₁ = 1

The energy of photon released when electron moves from the second energy level to the first energy level in hydrogen is calculated as following;

$\Delta E = R_H\times h\times C (\frac{1}{n_1^2 } - \frac{1}{n_2^2} )$

where;

Rh is the Rydberg constant

h is Plank's constant

C is the speed of light

$\Delta E = (1.0974 \times 10^7 \times 6.626 \times 10^{-34} \times 3\times 10^8)(\frac{1}{2^2} - \frac{1}{1^2} )\\\\\Delta E= 2.18 \times 10^{-18}(-0.75)\\\\\Delta E= - 1.635 \times 10^{-18} \ J$

The frequency of the light released is calculated as;

$E = hf$

where;

f is the frequency of the light;

$f = \frac{E}{h} \\\\f = \frac{1.635\times 10^{-18}}{6.626 \times 10^{-34}} \\\\f = 2.47 \times 10^{15} \ Hz$

Thus, the frequency of the light released is 2.47 x 10¹⁵ Hz.

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