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?
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/
Here, energy is E, Planks constant is h, the velocity of light is c and wavelength is .
Rearrange the formula to calculate the value of wavelength() as follows:
= 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:
= (6.626x10-34 J.s)(3.0 x 108 m/s)/(9.18 x 10-20 J)
= 2.165x 10-6 m
Now, The Rydberg's formula is as follows:
1/= 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/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.
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