QJEEAdv19Ch0fcd: JEE Advanced 2019 Chemistry - Class 11 JEEAdv19Ch0fcd Solution: The ground state energy of hydrogen atom is 13.6 eV. Consider…

Question

Verified Solution • 2025–26 Session moderate

The ground state energy of hydrogen atom is

-

13.6 eV. Consider an electronic state

\psi

of He⁺ whose energy, azimuthal quantum number and magnetic quantum number are

-

3.4 eV, 2 and 0, respectively.

Which of the following statement(s) is(are) true for the state

\psi

?

A It is a 4d state
B The nuclear charge experienced by the electron in this state is less than 2e, where e is the magnitude of the electronic charge
C It has 2 angular nodes
D It has 3 radial nodes

Accepted Answer

Given, ground state energy of hydrogen atom =

-

13.6 eV

Energy of He⁺ =

-

3.4 eV, Z = 2

Energy of He⁺, E =

- {{13.6 \times {Z^2}} \over {{n^2}}}eV

- 3.4eV = {{ - 13.6 \times {{(2)}^2}} \over {{n^2}}}

\Rightarrow

n =

\sqrt {{{ - 13.6 \times 4} \over {34}}}

\Rightarrow

n = 4

Given, azimuthal quantum number (l) = 2 (d

-

subshell)

Magnetic quantum number (m) = 0

\therefore

Angular nodes (l) = 2

Radial node = n

-

l

-

1 = 4

-

2

-

1 = 1

nl = 4d state

Hence, options (a), (c) are correct.

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