A proton and a deuteron are initially at rest | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

A deuteron is an isotope of hydrogen, having one proton and one neutron.

Proton and deuteron have the same charge. Let the charge be denoted by p.

M

Vedclass · Accepted Answer

They have same momentum

Vedclass · Answer

A deuteron is an isotope of hydrogen, having one proton and one neutron.

Proton and deuteron have the same charge. Let the charge be denoted by p.

Mass of proton is 1 amu, while mass of deuteron is 2 amu.

$m_{p}=1$ amu

$m_{d}=2 a m u$

Let they be accelerated by potential difference of $V$.

Kinetic energy of proton

$K_{p}=0.5 m_{p} v_{p}^{2}=e V$

Kinetic energy of deuteron

$K_{d}=0.5 m_{d} v_{d}^{2}=e V$

As we can see, $K_{p}=K_{d}$

$0.5 m_{d} v_{d}^{2}=0.5 m_{p} v_{p}^{2}$

$m_{d} v_{d}^{2}=m_{p} v_{p}^{2}$

Since $m_{d}=2 m_{p}$

$2 v_{d}^{2}=v_{p}^{2}$

$v_{p}=\sqrt{2} v_{d}$

So, velocity of proton is $\sqrt{2}$ times the velocity of deuteron.

Also.

$m_{p} v_{p}=0.5 m_{d} 	imes \sqrt{2} v_{d}=\frac{m_{d} v_{d}}{\sqrt{2}}$

Initial velocity of both the proton and deutron are zero. So, their initial momentum is zero.

Final momentum of proton and deutron are $m_{p} v_{p}$ and $m_{d} v_{d}$

So, we can find the change in momentum for both.

But we don't have any data to find the time taken for change in momentum.

since $F=\frac{d p}{d t}$ and we don't have dt

so we can't compare the force to which the two particles have been subjected.

A proton and a deuteron are initially at rest and are accelerated through the same potential difference. Which of the following is false concerning the final properties of the two particles ?