Question

the distance of the closest approach of an alpha particle fired at a nucleus with kinetic energy k is ro. the distance of the closest approach when the a particle is fired at the same nucleus with kinetic energy 2k will be

Answer 1

The distance of closest approach when an alpha particle is fired at the nucleus with twice the kinetic energy is given by the equation r' = 2^(1/3) * ro.

Step-by-step explanation:

The question asks for the distance of the closest approach when an alpha particle is fired at the same nucleus with twice the kinetic energy. The distance of closest approach, denoted as ro, is given by the equation r = ro * A^(1/3), where ro is a constant and A is the mass number of the nucleus.

Since the kinetic energy is directly proportional to the square of the velocity, if the kinetic energy is doubled, the velocity will increase by a factor of square root of 2.

Therefore, the mass number A in the equation r = ro * A^(1/3) will remain the same, but the value of ro will be multiplied by 2^(1/3).

Therefore, the distance of closest approach when the alpha particle is fired at the same nucleus with twice the kinetic energy will be: r' = 2^(1/3) * ro.