Question

An electron is at ground state of the $H$ atom. Minimum energy required to excite the $H$ atom into second excited state is:
A. $13.6\,eV$
B. $12.1\,eV$
C. $10.2\,eV$
D. $3.4\,eV$

Answer 1

Hint:Here we have to first find the energy required for the hydrogen atom to jump from the first state to the second by using the energy of the excited second state. The nuclear model of an atom was introduced by Rutherford's model, in which he clarified that a nucleus is surrounded by negatively charged electrons (positively charged).

Complete step by step answer:
The Bohr model of the atom was suggested in $1915$ by Neil Bohr. It came into being with the alteration of the model of an atom by Rutherford. Bohr changed this atomic structure model by demonstrating that electrons pass in fixed orbitals (shells) and not somewhere in between and he also demonstrated that each orbit (shell) has a fixed energy level. Basically, Rutherford explained an atom's nucleus and Bohr changed the concept into electrons and their energy levels.
One of Bohr’s postulates is:
An integer ($n = 1,2,3......$ ) known as the quantum number represents the energy levels. This quantum number spectrum begins from the side of the nucleus with the lowest energy level of $n = 1$. $N = 1,2,3,4$ orbits were allocated to be $K,L,M,N......$ shells and it is said that when an electron reaches the lowest energy level, it is in the ground state.
So, the energy required for an electron to jump to the second state is:
$
\Delta E = {E_3} - {E_1} \\
\Rightarrow\Delta E = \dfrac{{ - 13.6}}{{{3^2}}} - \left( { - 13.6} \right)\,\,\,\,\,\left[ {\because {\text{Energy}}\,{\text{of}}\,{\text{excited}}\,{\text{second}}\,{\text{state,}}\,{E_3} = \dfrac{{ - 13.6}}{{{3^2}}}} \right] \\
\Rightarrow\Delta E = - 1.5 + 13.6 \\
\therefore\Delta E = 12.1\,eV \\
$
Hence, option B is the answer.

Note:Here we have to see what atom is given in the question. Since, a hydrogen atom is given so we have taken the energy as $13.6$. If some other atom was given, then the answer would have been different.The model of Bohr consists of a small positively charged nucleus surrounded by negative electrons travelling in orbits around the nucleus. Bohr finds that there is more energy for an electron located further from the nucleus, and there is less energy for electrons nearest to the nucleus.