What is the energy in joules, required to shift the electron of the hydrogen atom from the first Bohr orbit to the fifth Bohr orbit? What is the wavelength of the light emitted when the electron returns to the ground state? The ground state electron energy is -2.18 x 10^(-11) ergs.
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Verified answer
(i) Energy = -Rh(1/n1²) - (1/n2²)
where,
n1 = initial orbit
n2 = final orbit
Rh = Rydberg constant (2.18 X 10⁻¹⁸)
First energy level (n1) = 1
Second energy level (n2) = 5
Energy = 2.18 X 10⁻¹⁸((1/1²) - (1/5²)
= 2.18 x 10⁻¹⁸((1/1) - (1/25)
= 2.18 x 10⁻¹⁸ x ((25-1)/25)
= 2.18 x 10⁻¹⁸ x ((24)/25)
= 2.18 x 10⁻¹⁸ x 24/25
= 52.3 x 10⁻¹⁸/25
= 2.09 x 10⁻¹⁸ J
∴ 2.09 x 10⁻¹⁸ J of energy is required to shift the electron of the hydrogen atom from the first Bohr orbit to the fifth Bohr orbit.
(ii) Wavelength (λ) = hc/E
where,
h = Plank constant
c = speed of light
E = energy
Wavelength
= 6.626 x 10^(-34) x 3.0 x 10⁸/2.09 x 10⁻¹⁸
= 19.87 x 10^(-26)/2.09 x 10⁻¹⁸
= 9.50 x 10⁻⁸ m
∴ Wavelength of the light emitted when the electron returns to the ground state is 9.50 x 10⁻⁸ m.
The ground state electron energy is the energy of the electron in the first orbit Bohr's orbit.
Where, n is equal to the number of orbits.
Now,
Energy has to be absorbed to shift the electron from Bohr's first orbit to the fifth.