Question

According to the bohr model what is the energy of an n=4 electron in a hydrogen atom?

Answer 1

According to Bohr's model, the energy of n = 4 electron in a hydrogen atom is 1.3625 × 10⁻¹⁹J

Bohr's Model of Hydrogen Atom

According to the postulates given by Bohr, electrons revolve around the nucleus in fixed circular orbits which are called stationary orbits or stationary states.

The energy of electrons in a stationary state is fixed and given by,

$E_n = \frac{-2\pi^2me^4}{n^2h^2} Z^2$

where, m = mass of electrons = 9.1 x 10⁻³¹ kg

e = charge on electron = 1.602 × 10⁻¹⁹ C

n = no of orbits

h = Planck's constant

Z= atomic number of H-like particles

After calculating all the constants values, we get

$E_n= \frac{-2.18 \times 10^-^{18}}{n^2} \times Z^2\\\\E_n= \frac{-2.18 \times 10^-^{18}}{4} \times 1^2$

= 0.13625 × 10⁻¹⁸

= 0.13625 × 10⁻¹⁹ J

Hence, the energy of n = 4 electron in a hydrogen atom is 1.3625 × 10⁻¹⁹J

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