The momentum of `alpha`-particles moving in a circular path of radius 10 cm in a perpendicular magnetic field of 0.05 tesla will be :

Options

A. `1.6xx10^(-20)km` m/s
B. `1.6xx10^(-21)kb` m/s
C. `1.6xx10^(-19)kg` m/s
D. `1.6xx10^(-18)kg` m/s

Explanation

To find the momentum of alpha particles moving in a circular path in a magnetic field, we can use the following steps:

### Step 1: Understand the relationship between magnetic force and centripetal force
When a charged particle moves in a magnetic field, it experiences a magnetic force that acts as the centripetal force keeping it in circular motion. The magnetic force \( F \) is given by:

\[ F = QvB \]

where:
- \( Q \) is the charge of the particle,
- \( v \) is the velocity of the particle,
- \( B \) is the magnetic field strength.

This magnetic force provides the necessary centripetal force \( F_c \) for circular motion:

\[ F_c = \frac{mv^2}{r} \]

where:
- \( m \) is the mass of the particle,
- \( r \) is the radius of the circular path.

### Step 2: Set the magnetic force equal to the centripetal force
Since the magnetic force acts as the centripetal force, we can set them equal to each other:

\[ QvB = \frac{mv^2}{r} \]

### Step 3: Rearrange to find momentum
The momentum \( p \) of the particle is given by:

\[ p = mv \]

From the equation \( QvB = \frac{mv^2}{r} \), we can express \( mv \) in terms of \( Q \), \( B \), and \( r \):

\[ mv = \frac{QBr}{v} \]

Multiplying both sides by \( v \):

\[ p = QBr \]

### Step 4: Substitute the known values
For an alpha particle:
- The charge \( Q \) is \( 2e \) (where \( e = 1.6 \times 10^{-19} \) C).
- The magnetic field \( B \) is \( 0.05 \) T.
- The radius \( r \) is \( 10 \) cm, which is \( 0.1 \) m.

Now substitute these values into the equation:

\[ p = QBr = (2 \times 1.6 \times 10^{-19} \, \text{C}) \times (0.05 \, \text{T}) \times (0.1 \, \text{m}) \]

### Step 5: Calculate the momentum
Now calculate the values:

\[ p = (3.2 \times 10^{-19}) \times (0.05) \times (0.1) \]

\[ p = 3.2 \times 10^{-20} \, \text{kg m/s} \]

### Step 6: Final result
Thus, the momentum of the alpha particles is:

\[ p = 3.2 \times 10^{-21} \, \text{kg m/s} \]