Question

(1) If energy of an electron in a hydrogen atom is -0.850 ev, in which main shell the said electron is present?​

Answer 1

Explanation:

Electrons in a hydrogen atom must be in one of the allowed energy levels. If an electron is in the first energy level, it must have exactly -13.6 eV of energy. If it is in the second energy level, it must have -3.4 eV of energy. An electron in a hydrogen atom cannot have -9 eV, -8 eV or any other value in between.

Answer 2

Given :

• Energy of electron in hydrogen atom = -0.850 ev

To Find :

• The main shell in which the electron is present

Solution :

The Energy of electron in nᵗʰ orbit of Hydrogen atom is given by ,

$\\ \star \: {\boxed{\purple{\sf{E_{n} = \dfrac{ - 13.6}{ {n}^{2}} \: ev }}}}$

Where ,

• n is orbit number

We are given that energy of electron in nᵗʰ orbit (let) as -0.850 ev.

$\\ : \implies \sf \: - 0.850 \: eV = \dfrac{ - 13.6}{ {n}^{2} } \: eV$

$\\ : \implies \sf \: - 0.850 \times {n}^{2} = - 13.6$

$\\ : \implies \sf \: {n}^{2} = \dfrac{ - 13.6}{ - 0.850}$

$\\ : \implies \sf \: {n}^{2} = 16$

$\\ : \implies \sf \: n = \sqrt{16}$

$\\ : \implies{\underline{\boxed{\pink{\mathfrak{n = 4}}}}} \: \bigstar$

Hence ,

• The main shell in which the given electron is present is 4th shell.