Which of the following is true ?

Options

A. The ionisation energy of a hydrogen -like species in its ground state is equal to the magnitude of energy of the orbit having `n = 1`
B. The ionisation energy of a hydrogen -like species in its ground state increases in principle to the positive charge in its nucleus
C. According to the uncertainty principle `Delta p Delta s le(h)/(4pi)`
D. The energy of an electron in a orbit of a multielectron atom depends only on the principle quantum number n

Explanation

To solve the question "Which of the following is true?", we need to evaluate each statement regarding hydrogen-like species and atomic structure principles.

### Step-by-Step Solution:

1. **Evaluate the First Statement:**
- The ionization energy of a hydrogen-like species in its ground state is equal to the magnitude of energy of the orbit having n = 1.
- The ionization energy for hydrogen-like species in the ground state (n=1) is given as 13.6 eV. The energy of the orbit for n=1 is calculated as:
\[ E = -\frac{13.6 \, \text{eV}}{n^2} = -\frac{13.6 \, \text{eV}}{1^2} = -13.6 \, \text{eV} \]
- The magnitude of this energy is 13.6 eV, which matches the ionization energy.
- **Conclusion:** This statement is true.

2. **Evaluate the Second Statement:**
- The ionization energy of a hydrogen-like species in its ground state increases in principle to the positive charge in its nucleus.
- The ionization energy is given by:
\[ E = 13.6 \times \frac{Z^2}{n^2} \]
For n=1, it becomes:
\[ E = 13.6 \times Z^2 \]
- While the ionization energy does depend on Z, it increases with the square of the atomic number (Z^2), not directly with Z.
- **Conclusion:** This statement is false.

3. **Evaluate the Third Statement:**
- According to the uncertainty principle, \(\Delta p \cdot \Delta x \geq \frac{h}{4\pi}\).
- The statement given is incorrect as it states \(\Delta p \cdot \Delta s\) instead of \(\Delta p \cdot \Delta x\).
- **Conclusion:** This statement is false.

4. **Evaluate the Fourth Statement:**
- The energy of an electron in an orbit of a multi-electron atom depends only on the principal quantum number n.
- In multi-electron atoms, the energy also depends on the azimuthal quantum number (l). Therefore, it does not depend solely on n.
- **Conclusion:** This statement is false.

### Final Conclusion:
Only the first option is true.

---