The number of waves made by an electron moving in an orbit having a maximum magnetic quantum number of +4 is

Options

A. 4
B. 5
C. 3
D. 6

Answer

To solve the question regarding the number of waves made by an electron moving in an orbit with a maximum magnetic quantum number of +4, we can follow these steps:

### Step 1: Understand the Quantum Numbers
- The magnetic quantum number (ml) can take values from -l to +l, where l is the azimuthal (or angular momentum) quantum number.
- The maximum value of ml is given as +4, which indicates that l must also be 4.

### Step 2: Determine the Azimuthal Quantum Number (l)
- Since ml = +4, the possible values of ml are: +4, +3, +2, +1, 0, -1, -2, -3, -4.
- This means that l = 4.

### Step 3: Relate l to the Principal Quantum Number (n)
- The relationship between the azimuthal quantum number (l) and the principal quantum number (n) is given by the formula:
\[ l = n - 1 \]
- Rearranging this gives:
\[ n = l + 1 \]

### Step 4: Calculate the Principal Quantum Number (n)
- Substituting l = 4 into the equation:
\[ n = 4 + 1 = 5 \]

### Step 5: Conclusion
- The principal quantum number (n) corresponds to the number of waves made by the electron in the orbit. Therefore, the number of waves made by the electron is 5.

### Final Answer
The number of waves made by an electron moving in an orbit having a maximum magnetic quantum number of +4 is **5**.

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