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Question
What is the energy in joule s required to shift the electron of the hydrogen atom from the first Bhor orbits to the fifth Bhor orbit and What is the wavelength of the light emitted when the electron return to the ground state? The ground state electron energy is -2.18?10^-11ergs
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Solution
Dear Student,
Grand state, n = 1, energy is given by,
E1= −2.18×10−11 ergs
Now, energy of the nth state for Hydrogen atom is given by,
En = E1 / n2
E5 = −2.18×10−11ergs / n2 (Here n = 5)
= −2.18×10−11ergs / (5)2
=−0.0872×10−11ergs
Energy required to go to the 5th orbit
=E5 − E1
= {−0.0872−(−2.18)}×10−11ergs
= 2.0928×10−11ergs
Now, 1erg = 10−7J
⇒ 2.0928×10−11ergs = 2.0928×10−18J
For wavelength,
1 / λ = R [ 1 / (n1)2 - 1 /( n2)2]
where, R = 1.0973×105cm−1 and n1 = 1, n2 = 5
⇒ 1 / λ = 1.0973×105 x [1− 1 / 25] cm−1
⇒ 1 / λ = 1.0534 x 105 cm−1
⇒ λ = 9.49 × 10−5 cm
or, ≃ 9.5×10−7 m
Regards
Grand state, n = 1, energy is given by,
E1= −2.18×10−11 ergs
Now, energy of the nth state for Hydrogen atom is given by,
En = E1 / n2
E5 = −2.18×10−11ergs / n2 (Here n = 5)
= −2.18×10−11ergs / (5)2
=−0.0872×10−11ergs
Energy required to go to the 5th orbit
=E5 − E1
= {−0.0872−(−2.18)}×10−11ergs
= 2.0928×10−11ergs
Now, 1erg = 10−7J
⇒ 2.0928×10−11ergs = 2.0928×10−18J
For wavelength,
1 / λ = R [ 1 / (n1)2 - 1 /( n2)2]
where, R = 1.0973×105cm−1 and n1 = 1, n2 = 5
⇒ 1 / λ = 1.0973×105 x [1− 1 / 25] cm−1
⇒ 1 / λ = 1.0534 x 105 cm−1
⇒ λ = 9.49 × 10−5 cm
or, ≃ 9.5×10−7 m
Regards
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