Bohr magneton Hg has the value

Options

A. `9.27 xx 10^(-14) A m^(2)`
B. `9.27 xx 10^(-18) A m^(2)`
C. `9.27 xx 10^(-24) A m^(2)`
D. `9.27 xx 10^(-21) A m^(2)`

Answer

To find the value of the Bohr magneton (μB) for mercury (Hg), we can follow these steps:

### Step 1: Understand the Definition of Bohr Magneton
Bohr magneton (μB) is a physical constant that represents the magnetic moment of an electron due to its spin and orbital angular momentum. It is defined as:

\[ \mu_B = \frac{e \hbar}{2m_e} \]

where:
- \( e \) = elementary charge (approximately \( 1.602 \times 10^{-19} \) coulombs)
- \( \hbar \) = reduced Planck's constant (approximately \( 1.055 \times 10^{-34} \) Js)
- \( m_e \) = rest mass of the electron (approximately \( 9.109 \times 10^{-31} \) kg)

### Step 2: Substitute the Values into the Formula
Now, we can substitute the known values into the formula to calculate the Bohr magneton:

\[ \mu_B = \frac{(1.602 \times 10^{-19} \, \text{C})(1.055 \times 10^{-34} \, \text{Js})}{2(9.109 \times 10^{-31} \, \text{kg})} \]

### Step 3: Calculate the Numerator
Calculating the numerator:

\[ 1.602 \times 10^{-19} \times 1.055 \times 10^{-34} = 1.692 \times 10^{-53} \, \text{CJs} \]

### Step 4: Calculate the Denominator
Calculating the denominator:

\[ 2 \times 9.109 \times 10^{-31} = 1.822 \times 10^{-30} \, \text{kg} \]

### Step 5: Divide the Numerator by the Denominator
Now, we divide the numerator by the denominator to find the value of μB:

\[ \mu_B = \frac{1.692 \times 10^{-53}}{1.822 \times 10^{-30}} \approx 9.27 \times 10^{-24} \, \text{A m}^2 \]

### Step 6: Conclusion
Thus, the value of the Bohr magneton (μB) is approximately:

\[ \mu_B \approx 9.27 \times 10^{-24} \, \text{A m}^2 \]

This value is consistent with the known value of the Bohr magneton.