The number of waves made by a Bohr electron in an orbit of maximum magnetic quantum number + 2 is

Options

A. 3
B. 0
C. 2
D. 1

Answer

To solve the question regarding the number of waves made by a Bohr electron in an orbit with a maximum magnetic quantum number of +2, we can follow these steps:

### Step 1: Understand the Quantum Numbers
The magnetic quantum number (m) can take values from -l to +l, where l is the azimuthal quantum number. Given that m = +2, we can deduce the value of l.

### Step 2: Determine the Azimuthal Quantum Number (l)
Since the maximum value of m is +l, if m = +2, then:
- The possible values of m are: -l, ..., 0, ..., +l.
- Therefore, for m = +2, l must be equal to 2.

### Step 3: Calculate the Principal Quantum Number (n)
The principal quantum number (n) is related to the azimuthal quantum number (l) by the formula:
\[ n = l + 1 \]
Substituting the value of l:
\[ n = 2 + 1 = 3 \]

### Step 4: Determine the Number of Waves
In a Bohr model, the number of waves made by an electron in an orbit is equal to the principal quantum number (n). Thus, if n = 3, the number of waves made by the electron in this orbit is:
\[ \text{Number of waves} = n = 3 \]

### Final Answer
The number of waves made by a Bohr electron in an orbit with a maximum magnetic quantum number of +2 is **3**.

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