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An electron in a hydrogen atom absorbs 9.18 x 10 -20 J of energy. If the...

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?

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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/\lambdaR]

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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