A particular hydrogen like atom has its ground state Binding energy `= 122.4 eV`. It is in ground state. Then

Options

A. Its atomic number is 5
B. an electron fo 90 eV can excite it
C. an electron of kinetic energy 45. 9 eV can be brought to almost rest by this atom
D. an electron fo kinetic energy nearly 2.6 eV may emerge from the atom when electron of kinetic energy 125 eV collides with this atom

Answer

To solve the problem, we need to find the atomic number (Z) of a hydrogen-like atom given its ground state binding energy of 122.4 eV. The formula for the binding energy of an electron in a hydrogen-like atom is given by:

\[ E_n = -\frac{13.6 \, Z^2}{n^2} \, \text{eV} \]

where:
- \(E_n\) is the binding energy,
- \(Z\) is the atomic number,
- \(n\) is the principal quantum number (for ground state, \(n = 1\)).

### Step 1: Substitute the values into the formula
For the ground state (\(n = 1\)), the equation becomes:

\[ E_1 = -\frac{13.6 \, Z^2}{1^2} \]

Given that the binding energy is 122.4 eV, we can set up the equation:

\[ -13.6 \, Z^2 = -122.4 \]

### Step 2: Solve for \(Z^2\)
Removing the negative signs gives:

\[ 13.6 \, Z^2 = 122.4 \]

Now, divide both sides by 13.6:

\[ Z^2 = \frac{122.4}{13.6} \]

### Step 3: Calculate \(Z^2\)
Calculating the right side:

\[ Z^2 = 9 \]

### Step 4: Find \(Z\)
Taking the square root of both sides:

\[ Z = \sqrt{9} = 3 \]

### Conclusion
The atomic number \(Z\) of the hydrogen-like atom is 3.

### Step 5: Analyze the options
Now we analyze the options provided in the question:
1. **Atomic number is 5** - Incorrect, we found \(Z = 3\).
2. **An electron of 90 eV can excite it** - Incorrect, as the binding energy is 122.4 eV.
3. **An electron of kinetic energy 45.9 eV can be brought to almost rest by the atom** - Correct, since it is less than the binding energy.
4. **An electron of kinetic energy nearly 2.6 eV may emerge from an atom when an electron of kinetic energy 125 eV collides with the atom** - Correct, since \(125 - 122.4 = 2.6\).

Thus, the correct options are 3 and 4.