Q102 / 200 · MHT CET - Medical 2026 (25 April Shift 1) · Chemistry
Calculate the energy associated with an electron in the first orbit of hydrogen atom?
- Correct answerA$-2.18 \times 10^{-18}\ \text{J}$
- B$52.9\ \text{J}$
- C$-1.09 \times 10^{-18}\ \text{J}$
- D$2.18 \times 10^{-18}\ \text{J}$
Solution
The energy of an electron in the $n^{\text{th}}$ orbit of a hydrogen-like species is given by the Bohr model as:
$E_n = -2.18 \times 10^{-18} \times \dfrac{Z^2}{n^2}\ \text{J}$
For a hydrogen atom, the atomic number $Z = 1$.
For the first orbit, the principal quantum number $n = 1$.
Substituting these values into the formula, we get:
$E_1 = -2.18 \times 10^{-18} \times \dfrac{1^2}{1^2}\ \text{J}$
$E_1 = -2.18 \times 10^{-18}\ \text{J}$
Answer: $-2.18 \times 10^{-18}\ \text{J}$
$E_n = -2.18 \times 10^{-18} \times \dfrac{Z^2}{n^2}\ \text{J}$
For a hydrogen atom, the atomic number $Z = 1$.
For the first orbit, the principal quantum number $n = 1$.
Substituting these values into the formula, we get:
$E_1 = -2.18 \times 10^{-18} \times \dfrac{1^2}{1^2}\ \text{J}$
$E_1 = -2.18 \times 10^{-18}\ \text{J}$
Answer: $-2.18 \times 10^{-18}\ \text{J}$
Hence, the correct answer is option: 'A'.