Physics Q43 – JEE-MAIN 2025

Considering Bohr's atomic model for hydrogen atom : (A) the energy of H atom in ground state is same as energy of

H e^{+}

ion in its first excited state. (B) the energy of H atom in ground state is same as that for

L i^{+ +}

ion in its second excited state. (C) the energy of H atom in its ground state is same as that of

H e^{+}

ion for its ground state. (D) the energy of

H e^{+}

ion in its first excited state is same as that for

L i^{+ +}

ion in its ground state. Choose the correct answer from the options given below :

Recall the formula for the energy of an electron in the $n$ -th orbit of a hydrogen-like atom.

🥷

Ninja Strategy•Direct Evaluation and Elimination

Evaluate each statement (A, B, C, D) using the Bohr energy formula. Once false statements are identified, eliminate options that contain them.

● Video Walkthrough

Step 1: Recall Bohr's Energy Formula✦ Active

The energy of an electron in the $n$ -th orbit of a hydrogen-like atom with atomic number $Z$ is given by:

E_{n} = - 13.6 \frac{Z^{2}}{n^{2}} eV

Step 2: Evaluate Each Statement○ Expand

Let's calculate the energy for each specified state:

(A) H atom (ground state): Z = 1, n = 1 ⟹ E_{H} (n = 1) = - 13.6 \frac{1^{2}}{1^{2}} = - 13.6 eV

{He}^{+} ion (first excited state): Z = 2, n = 2 ⟹ E_{H e^{+}} (n = 2) = - 13.6 \frac{2^{2}}{2^{2}} = - 13.6 eV

Statement (A) is TRUE as $E_{H} (n = 1) = E_{H e^{+}} (n = 2)$ .

(B) H atom (ground state): E_{H} (n = 1) = - 13.6 eV

{Li}^{+ +} ion (second excited state): Z = 3, n = 3 ⟹ E_{L i^{+ +}} (n = 3) = - 13.6 \frac{3^{2}}{3^{2}} = - 13.6 eV

Statement (B) is TRUE as $E_{H} (n = 1) = E_{L i^{+ +}} (n = 3)$ .

(C) H atom (ground state): E_{H} (n = 1) = - 13.6 eV

{He}^{+} ion (ground state): Z = 2, n = 1 ⟹ E_{H e^{+}} (n = 1) = - 13.6 \frac{2^{2}}{1^{2}} = - 54.4 eV

Statement (C) is FALSE as $E_{H} (n = 1) \neq E_{H e^{+}} (n = 1)$ .

{(D) He}^{+} ion (first excited state): E_{H e^{+}} (n = 2) = - 13.6 eV

{Li}^{+ +} ion (ground state): Z = 3, n = 1 ⟹ E_{L i^{+ +}} (n = 1) = - 13.6 \frac{3^{2}}{1^{2}} = - 122.4 eV

Statement (D) is FALSE as $E_{H e^{+}} (n = 2) \neq E_{L i^{+ +}} (n = 1)$ .

💡 Teacher's Secret Hint

Pay close attention to the atomic number $Z$ and the principal quantum number $n$ for each species and state.

Step 3: Identify Correct Option○ Expand

Only statements (A) and (B) are correct. Therefore, the option that includes (A) and (B) only is the correct answer.

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Physics Question 43 – JEE-MAIN 2025