A particle is moving 5 times as fast as an electron. The ratio of the de-Broglie wavelength of the particle to that of the electron is `1.878 xx10^(-4) ` . The mass of the particle is close to :

Options

A. `4.8 xx 10^(-27)` kg
B. `9.1 xx10^(-31)` kg
C. `9.7 xx10^(-28)` kg
D. `1.2 xx10^(-28)` kg

Explanation

To solve the problem, we need to find the mass of the particle given the information about its velocity and the ratio of its de-Broglie wavelength to that of an electron.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
- The particle is moving 5 times as fast as an electron.
- Let the velocity of the electron be \( v_e \) and the velocity of the particle be \( v_p \).
- Therefore, \( v_p = 5 v_e \).

2. **De-Broglie Wavelength Formula**:
- The de-Broglie wavelength \( \lambda \) is given by the formula:
\[ \lambda = \frac{h}{mv} \]
where \( h \) is Planck's constant, \( m \) is mass, and \( v \) is velocity.

3. **Setting Up the Ratio**:
- The ratio of the de-Broglie wavelengths of the particle and the electron is given as:
\[ \frac{\lambda_p}{\lambda_e} = 1.878 \times 10^{-4} \]
- Using the de-Broglie wavelength formula, we can express this ratio as:
\[ \frac{\lambda_p}{\lambda_e} = \frac{h/m_p v_p}{h/m_e v_e} = \frac{m_e v_e}{m_p v_p} \]

4. **Substituting the Velocity Relationship**:
- Since \( v_p = 5 v_e \), we can substitute this into the ratio:
\[ \frac{\lambda_p}{\lambda_e} = \frac{m_e v_e}{m_p (5 v_e)} = \frac{m_e}{5 m_p} \]

5. **Equating the Ratios**:
- Now we equate the two expressions for the ratio:
\[ \frac{m_e}{5 m_p} = 1.878 \times 10^{-4} \]

6. **Solving for the Mass of the Particle**:
- Rearranging gives us:
\[ m_p = \frac{m_e}{5 \times (1.878 \times 10^{-4})} \]
- We know the mass of the electron \( m_e \) is approximately \( 9.1 \times 10^{-31} \) kg.
- Substituting this value in:
\[ m_p = \frac{9.1 \times 10^{-31}}{5 \times 1.878 \times 10^{-4}} \]

7. **Calculating the Mass**:
- First, calculate \( 5 \times 1.878 \times 10^{-4} \):
\[ 5 \times 1.878 \times 10^{-4} = 9.39 \times 10^{-4} \]
- Now calculate \( m_p \):
\[ m_p = \frac{9.1 \times 10^{-31}}{9.39 \times 10^{-4}} \approx 9.7 \times 10^{-28} \text{ kg} \]

### Final Answer:
The mass of the particle is approximately \( 9.7 \times 10^{-28} \) kg.