Question

In a nuclear physics experiment, a proton (mass 1.67×10^(−27)kg, charge +e=+1.60×10^(−19)C) is fired directly at a target nucleus of unknown charge. (You can treat both objects as point charges, and assume that the nucleus remains at rest.) When it is far from its target, the proton has speed 2.50×10^6 m/s. The proton comes momentarily to rest at a distance 5.31×10^(−13)m from the center of the target nucleus, then flies back in the direction from which it came. What is the number of the protons the nucleus has? Assume no electron cloud is there, ε0=8.85x10^(-12) C^2/(Nm^2)

Answer 1

The given question is incomplete. The complete question is as follows.

In a nuclear physics experiment, a proton (mass
`1.67 * 10^(-27)`kg, charge +e =
`+1.60 * 10^(-19)` C) is fired directly at a target nucleus of unknown charge. (You can treat both objects as point charges, and assume that the nucleus remains at rest.) When it is far from its target, the proton has speed
`2.50 * 10^6` m/s. The proton comes momentarily to rest at a distance
`5.31 * 10^(-13)` m from the center of the target nucleus, then flies back in the direction from which it came. What is the electric potential energy of the proton and nucleus when they are
`5.31 * 10^(-13)` m apart?

Step-by-step explanation:

The given data is as follows.

Mass of proton =
`1.67 * 10^(-27)` kg

Charge of proton =
`1.6 * 10^(-19) C`

Speed of proton =
`2.50 * 10^(6) m/s`

Distance traveled =
`5.31 * 10^(-13) m`

We will calculate the electric potential energy of the proton and the nucleus by conservation of energy as follows.

`(K.E + P.E)_(initial)` =
`(K.E + P.E)_(final)`

`((1)/(2) m_(p)v^(2)_(p)) = ((kq_(p)q_(t))/(r) + 0)`

where,
`(kq_(p)q_(t))/(r) = U = Electric potential energy`

U =
`((1)/(2)m_(p)v^(2)_(p))`

Putting the given values into the above formula as follows.

U =
`((1)/(2)m_(p)v^(2)_(p))`

=
`((1)/(2) * 1.67 * 10^(-27) * (2.5 * 10^(6))^(2))`

=
`5.218 * 10^(-15) J`

Therefore, we can conclude that the electric potential energy of the proton and nucleus is
`5.218 * 10^(-15) J`.