Which of the following is false?

Options

A. The energy of an electron in an orbital of a hydrogen -like species depends only on the principle quantum number n
B. The angular momentum of electron in an orbital of a multielectron atom depends on the quantum number l and m
C. The experiment of angular momentum of an orbital is given as `sqrt(l(1 - 1)) ((h)/(2pi))`
D. The z-component of angular momentum of an electron in an orbital is given as `m ((h)/(12pi))`

Explanation

To determine which statement is false, we will analyze each statement one by one.

### Step 1: Analyze the First Statement
**Statement:** The energy of an electron in an orbital of a hydrogen-like species depends only upon the principal quantum number \( n \).

**Analysis:** This statement is true. In hydrogen-like species (which have only one electron), the energy levels depend solely on the principal quantum number \( n \). The energy increases as \( n \) increases.

**Conclusion:** This statement is true.

### Step 2: Analyze the Second Statement
**Statement:** The angular momentum of an electron in an orbital of a multi-electron atom depends upon quantum numbers \( L \) and \( M \).

**Analysis:** This statement is also true. The angular momentum in multi-electron systems is determined by the azimuthal quantum number \( L \) and the magnetic quantum number \( M \).

**Conclusion:** This statement is true.

### Step 3: Analyze the Third Statement
**Statement:** The expression for angular momentum of an orbital is given by \( \sqrt{L(1 - 1)} \frac{h}{2\pi} \).

**Analysis:** This statement is false. The correct expression for the orbital angular momentum is given by \( \sqrt{L(L + 1)} \frac{h}{2\pi} \). The formula provided in the statement is incorrect.

**Conclusion:** This statement is false.

### Step 4: Analyze the Fourth Statement
**Statement:** The \( z \) component of angular momentum of an electron in an orbital is given by \( M \frac{h}{2\pi} \).

**Analysis:** This statement is true. The \( z \) component of angular momentum is indeed given by \( M \frac{h}{2\pi} \), where \( M \) is the magnetic quantum number.

**Conclusion:** This statement is true.

### Final Conclusion
The false statement among the options provided is the third statement regarding the expression for angular momentum.

### Answer: The third statement is false.

---