Question

An electron in a hydrogen atom absorbs 9.18 x 10 -20 J of energy. If the electron originated at energy level 4, to what level was it excited?

Answer 1

When an electron absorbs energy, it will excite from a lower energy level to the higher energy level.

Energy absorbed(E) = 9.18 x 10^-20 J

Lower energy level(n₁) = 4

Determine the wavelength by using the formula as follows:

E = hc/$\lambda$

Here, energy is E, Planks constant is h, the velocity of light is c and wavelength is $\lambda$.

Rearrange the formula to calculate the value of wavelength($\lambda$) as follows:

$\lambda$= hc/E

The velocity of light(c) = 3.0 x 10⁸ m/s

Planks constant(h) = 6.626 x 10^-34 J.s

Substitute the known values and solve for wavelength as follows:

$\lambda$= (6.626x10^-34 J.s)(3.0 x 10⁸ m/s)/(9.18 x 10^-20 J)

$\lambda$= 2.165x 10^-6 m

Now, The Rydberg's formula is as follows:

1/$\lambda$= R [1/n₁² - 1/n₂² ]

Here, R = 1.097 x 10⁷ m/s

Rearrange the formula for (1/n₂²) as follows:

1/n₂² = [1/n₁² - 1/$\lambda$R]

Substitute the known values and solve for n₂ as follows:

1/n₂² = [1/4² - 1/(3.0 x 10⁸ m/s)(9.18 x 10^-20 J)]

1/n₂² = [1/16 - 1/(2.165x 10^-6 m)(1.097 x 10⁷ m^-1)]

1/n₂² = 0.0625 - 0.04210

1/n₂² = 0.0204

n₂ = 7

Thus, the electron excited to the energy level 7.