Question 18

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 and what is the wavelength of the light emitted when the electron returns to the ground state? The ground state electron energy is –2.18 × 10–11 ergs.

Answer

Ground state energy (E1) = – 2.18 × 10–11 ergs (given)

 = –2.18 × 10–11 × 10–7 J

 = – 2.18 × 10–18 J

Also the energy required to shift the electron from n = 1 to n = 5 is given as ΔE = E5 – E1

The expression for the energy of hydrogen of electron is

En = -2π2me4Z2/n2h2

Where m= mass of electrons

Z=atomic mass of atom 

e = charge of electron

h = planck’s constant

Now putting the values in the equation ΔE = E5 – E1 we get

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