A proton (mass mp), a deuteron (m = 2mp, Q = e), and an alpha particle (m = 4mp, Q = 2e), are accelerated by the same potential difference V and then enter a uniform magnetic field B where they move in circular paths perpendicular to B. Determine the radius of the paths for the deuteron and alpha particle in terms of that for the proton.

Answer with Explanation:

We are given that

Mass of deuteron=

Charge, Q=e

Mass of alpha particle=

Charge,q=2e

Magnetic field=B

Mass of proton=

Let radius of path of proton=r

Using the formula

Velocity of proton=

Centripetal force =Magnetic force

Radius of proton,

Radius of deuteron,

Radius of alpha particle,

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.

c. newton's third law of motion