Question

Total energy of Hydrogen like species is given as -54.4 eV/atom. The value of 'n' and 'Z' respectively are :

• A. 1,2
• B. 2,2
• C. 2,1
• D. 1,1

Hint:

For hydrogen-like atoms, the total energy is inversely proportional to the square of the principal quantum number \( n \) and directly proportional to the square of the atomic number \( Z \).

Answer 1

The Correct Option is A

Step 1: Understanding the given data.
The total energy of a hydrogen-like atom is given by the equation: \[ E = - \frac{13.6 Z^2}{n^2} \, \text{eV} \] Where:
- \( E \) is the total energy
- \( Z \) is the atomic number
- \( n \) is the principal quantum number

Step 2: Applying the given energy.
We are given that the total energy \( E = - 54.4 \, \text{eV} \). Substituting this into the energy formula: \[ -54.4 = - \frac{13.6 Z^2}{n^2} \]
Step 3: Solving the equation.
Simplifying the equation: \[ 54.4 = \frac{13.6 Z^2}{n^2} \] \[ \frac{54.4}{13.6} = \frac{Z^2}{n^2} \] \[ 4 = \frac{Z^2}{n^2} \]
Step 4: Finding the values of \( Z \) and \( n \).
From the equation, we get: \[ Z^2 = 4n^2 \] Thus, \( Z = 2 \) and \( n = 1 \), which satisfies the equation.
Step 5: Conclusion.
The correct values for \( n \) and \( Z \) are \( n = 1 \) and \( Z = 2 \). Final Answer: (A) 1,2