What is the wavelength (in m) of a particle of mass `6.62 xx 10^(-29) g` moving with a velocity of `10^(3) ms^(-1)`?

Options

A. `6.62 xx 10^(-4)`
B. `6.12 xx 10^(-3)`
C. `10^(-5)`
D. `10^(5)`

Explanation

To find the wavelength of a particle using the de Broglie equation, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Mass of the particle, \( m = 6.62 \times 10^{-29} \) g
- Velocity of the particle, \( v = 10^{3} \) m/s

2. **Convert Mass from Grams to Kilograms**:
- Since the standard unit of mass in the SI system is kilograms, we need to convert grams to kilograms.
\[ m = 6.62 \times 10^{-29} \text{ g} = 6.62 \times 10^{-29} \text{ g} \times \frac{1 \text{ kg}}{1000 \text{ g}} = 6.62 \times 10^{-32} \text{ kg} \]

3. **Use the de Broglie Wavelength Formula**:
- The de Broglie wavelength \( \lambda \) is given by the formula:
\[ \lambda = \frac{h}{mv} \]
where \( h \) is Planck's constant, \( h = 6.62 \times 10^{-34} \text{ kg m}^2/\text{s} \).

4. **Substitute the Values into the Formula**:
\[ \lambda = \frac{6.62 \times 10^{-34} \text{ kg m}^2/\text{s}}{(6.62 \times 10^{-32} \text{ kg})(10^{3} \text{ m/s})} \]

5. **Calculate the Denominator**:
\[ mv = (6.62 \times 10^{-32} \text{ kg})(10^{3} \text{ m/s}) = 6.62 \times 10^{-29} \text{ kg m/s} \]

6. **Calculate the Wavelength**:
\[ \lambda = \frac{6.62 \times 10^{-34}}{6.62 \times 10^{-29}} = 10^{-5} \text{ m} \]

### Final Answer:
The wavelength \( \lambda \) of the particle is \( 10^{-5} \) m.

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