If the de-Broglie wavelength of a particle of mass m is 100 times its velocity then its value in terms of its mass (m) and Planck's constant (h) is

Options

A. `1/(10)sqrt(m/h)`
B. `10sqrt(h/m)`
C. `1/(10)sqrt(h/m)`
D. `10sqrt(m/h)`

Answer

To solve the problem step by step, we will use the de Broglie wavelength formula and the information given in the question.

### Step 1: Understand the de Broglie Wavelength Formula
The de Broglie wavelength (\( \lambda \)) of a particle is given by the formula:
\[ \lambda = \frac{h}{mv} \]
where:
- \( \lambda \) is the de Broglie wavelength,
- \( h \) is Planck's constant,
- \( m \) is the mass of the particle,
- \( v \) is the velocity of the particle.

### Step 2: Set Up the Equation Based on the Given Information
According to the problem, the de Broglie wavelength is 100 times the velocity:
\[ \lambda = 100v \]

### Step 3: Substitute the Expression for Wavelength
Now we can substitute this expression for \( \lambda \) into the de Broglie wavelength formula:
\[ 100v = \frac{h}{mv} \]

### Step 4: Rearrange the Equation
To eliminate \( v \) from the denominator, multiply both sides by \( mv \):
\[ 100mv^2 = h \]

### Step 5: Solve for Velocity
Now, we can solve for \( v^2 \):
\[ v^2 = \frac{h}{100m} \]

### Step 6: Take the Square Root
Taking the square root of both sides gives us:
\[ v = \sqrt{\frac{h}{100m}} \]

### Step 7: Simplify the Expression
We can simplify this further:
\[ v = \frac{1}{10} \sqrt{\frac{h}{m}} \]

### Conclusion
Thus, the value of the velocity \( v \) in terms of mass \( m \) and Planck's constant \( h \) is:
\[ v = \frac{1}{10} \sqrt{\frac{h}{m}} \]