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Question

Energy of an electron is given by, E=2.178×1018(Z2n2)J. Wavelength of light required to excite an electron in hydrogen atom from level n=1 to n=2 will be:
(h=6.62×1034Jsandc=3×108ms1)

A
6.500×107m
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B
8.500×107m
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C
1.214×107m
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D
2.816×107m
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Solution

The correct option is C 1.214×107m
Explanation:

Given

E=2.178×1018J[Z2n2](1)

For hydrogen atom Z=1

ΔE=E2E1(2)

E1=2.178×1018[112](3)

E2=2.178×1018[122](4)

Substitute equation (3) and (4) value in equation(2)

ΔE=E2E1=(2.178×1018[122])(2.178×1018[112])=2.178×1018[122112]

ΔE=E2E1=2.178×1018[122112](5)

ΔE=hcλ(6)

where,

h=Planck's constant=6.62×1034

c=Velocity of light=3×108

λ=wavelength=?
Equate equation (5) and (6), then solve them to find the wavelength.

ΔE=E2E1=hcλ

2.178×1018[122112]=6.62×1034×3×108λ

1.6335×1018=1.986×1025λ


λ=1.986×10251.6335×10181.214×107m


λ=1.214×107m

Hence the correct answer is option (C).


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