Question

the energy of hydrogen atom in the ground state is -13.6 EV its energy corresponding to the quantum number N = 5 is

Answer 1

En=-13.6*z*z/n*n

=-13.6*1/25

=-0.54ev

Answer 2

Energy corresponding to the quantum number n = 5 is -0.544 eV

Explanation:

Using Rydberg equation:

$E=\frac{R_H}{n^2} \times Z^2$ (1)

Where,

E = energy

$R_H$ = Rydberg's Constant

$n$ = 1 (for ground state)

Z= atomic number = 1 (for hydrogen)

Putting the values, in above equation, we get

$-13.6eV=\frac{R_H}{1^2} \times 1^2$

${R_H}=-13.6eV$

For n= 5, energy can be calculated by using equation (1)

$E=\frac{-13.6eV}{5^2} \times 1^2$

$E=-0.544eV$

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