Question

In the hydrogen atom, what is the total energy of an electron that is in an orbit that has a radius of 8.784 × 10^(-10) m?

Answer 1

Answer:

The total energy of an electron in H atom is $1.31\times10^{-19}\ J$.

Explanation:

Given that,

Radius $R=8.784\times10^{-10}\ m$

We need to calculate the orbit number

Using formula of radius

$R=a_{0}n^2$

$n^2=\dfrac{R}{a_{0}}$

Where, a₀ = boar radius

n = orbit number

Put the value into the formula

$n^2=\dfrac{8.784\times10^{-10}}{0.529\times10^{-10}}$

$n=\sqrt{\dfrac{8.784\times10^{-10}}{0.529\times10^{-10}}}$

$n=4.07$

We need to calculate the total energy of an electron in H atom

Using formula of energy

$E=-\dfrac{13.6}{n^2}$

Put the value into the formula

$E=\dfrac{-13.6}{16.60}\ ev$

$E=0.8192\times1.6\times10^{-19}$

$E=1.31\times10^{-19}\ J$

Hence, The total energy of an electron in H atom is $1.31\times10^{-19}\ J$.