Question

The energy of electron in the second orbit of hydrogen atom is -328 kille joule per mole find out the energy of electron in the fourth orbit of hydrogen atom?​

Answer 1

Answer:

-82 kilo joule per mole

Explanation:

Given

Energy of electron in the second orbit of the atom = -328 kilo joule/mole

Or

E 2 = -328 kilo joule/mole

E 4 = ????

We know that

$En = - 13.6 \frac{ {Z}^{2} }{ {n}^{2} } ev/atom$

According to Question

$= > \frac{E2}{E4} = \frac{ - 13.6 \times \frac{ {1}^{2} }{ {2}^{2} } }{ - 13.6 \times \frac{ {1}^{2} }{ {4}^{2} } }$

On cancellation

$= > \frac{E2}{E4} = \frac{ \cancel{- 13.6} \times \frac{ \cancel{{1}^{2}} }{ {2}^{2} } }{ \cancel{- 13.6} \times \frac{ \cancel{{1}^{2}} }{ {4}^{2} } } \\ = > \frac{E2}{E4} = \frac{ {4}^{2} }{ {2}^{2} } \\ = > \frac{E2}{E4} = \frac{ \cancel{16}}{ \cancel{4}} \\ = > \frac{E2}{E4} = \frac{4}{1}$

On putting value of E 2

$= > \frac{ - 328}{E4} = \frac{4}{1} \\ = > E4 = - \frac{ \cancel{328}}{ \cancel{4} } \\ = > \huge \boxed{E4 = - 82 \: kj/mole}$

Hence

Energy of Electron in the fourth orbit will be -82 kilo joule / mole.

Answer 2

Correct Question—

The energy of electron in the second orbit of hydrogen atom is -328 kj/mole

.Find out the energy of electron in the fourth orbit of hydrogen atom?

--------------------------------------------------

$\bold {\huge {Your ~answer :-}}$

$\bf\huge\boxed{-82\:kj/mol}$

Given —

E1= - 328 kj/mol

To find E4 = ?

Now

We know that

The energy of an electron is Bohr's orbit of hydrogen atom is given by

$n = \frac{2\pi {}^{2} \: me {}^{4}z {}^{4} }{ {n}^{2}h {}^{2}(4\pi \: epl) {}^{2} } \\ n = - 13.6 \frac{ {z}^{2} }{ {n}^{2} } ev \\ n = - 328 \frac{z {}^{2} }{ {n}^{2} } \frac{kj}{mol} \\ e1 = - 328 \\ here \: = 1 \: z = 1$

Energy of second bohr orbit of the hydrogen atom is -328 kj/mol.

As from above formula The energy of hydrogen atom is inversely proportional to square of principle quantum no.

Therefore, the energy of fourth bohr orbit would be=(-328/4)= -82 kj/mol

As If the electron jumps to fourth orbit from second orbit then it will absorb -82 kj/mol energy.

Thus, we can conclude energy of hydrogen atom by Bohr's atomic model.

THNXX☺☺