The neutron, proton, electron and alpha particle are moving with equal kinetic energies. How can the particles be arranged in the increaseing order of their velocities?

Options

A. alpha particle -neutron proton - electron
B. proton - electron - neutron - alpha paraticle
C. electron - ptoton - neutron - alpha paraticle
D. neutron - proton - electron - alpha paraticle

Explanation

To determine the increasing order of velocities of the neutron, proton, electron, and alpha particle when they all have the same kinetic energy, we can follow these steps:

### Step 1: Understand the relationship between kinetic energy and velocity
The kinetic energy (KE) of a particle is given by the formula:
\[ KE = \frac{1}{2} mv^2 \]
where \(m\) is the mass of the particle and \(v\) is its velocity.

### Step 2: Rearranging the formula
Since we know that the kinetic energy is constant for all particles, we can rearrange the formula to express velocity in terms of kinetic energy and mass:
\[ v = \sqrt{\frac{2 \cdot KE}{m}} \]
From this equation, we can see that velocity \(v\) is inversely proportional to the square root of the mass \(m\):
\[ v \propto \frac{1}{\sqrt{m}} \]

### Step 3: Identify the masses of the particles
Now, we need to identify the masses of the particles involved:
- Mass of electron (\(m_e\)) is the smallest.
- Mass of proton (\(m_p\)) is larger than that of the electron.
- Mass of neutron (\(m_n\)) is similar to that of the proton but slightly larger.
- Mass of alpha particle (\(m_{\alpha}\)) is significantly larger than the other three.

### Step 4: Compare the velocities based on mass
Since the velocity is inversely proportional to the square root of mass, the particle with the smallest mass will have the highest velocity, and the particle with the largest mass will have the lowest velocity. Thus, we can arrange the particles in order of increasing mass:
- Electron (smallest mass, highest velocity)
- Proton
- Neutron
- Alpha particle (largest mass, lowest velocity)

### Step 5: Write the increasing order of velocities
Based on the above analysis, the increasing order of velocities is:
\[ v_{\alpha} < v_{n} < v_{p} < v_{e} \]
This means that the order from lowest to highest velocity is:
- Alpha particle
- Neutron
- Proton
- Electron

### Final Answer
The increasing order of velocities is:
**Alpha particle < Neutron < Proton < Electron**