Pinging Protons

Fission is the process of emitting particles from an unstable radioactive nucleus. This releases quite a bit of energy. Suppose you wanted to instead add a particle, such as a proton, to a nucleus. This is difficult as the electric force the proton feels from the nucleus will tend to repel the proton. If you fired a proton directly towards an iron nucleus, what is the magnitude in Newtons of the force the proton would feel if it is 2 fm from the surface of the iron nucleus?

Assumptions
k = 9 × 1 0 9 k=9 \times 10^9
Model an iron nucleus as a sphere of radius 3 fm.


The answer is 240.21.

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3 solutions

Snehdeep Arora
Mar 24, 2014

An iron nucleus has 26 protons each having a charge of 1.6 × 1 0 19 1.6 \times 10^{-19} , which is the charge on one proton.Using Coulomb's law force on the proton = ( k q 1 q 2 ) / r 2 (kq_1q_2)/r^2 where r is the distance between the charges.Here q 1 q_1 = 26×1.6×10^(-19) and. q 2 q_2 = 1.6×10^(-19) and. r=5×10^(-15). Plugging in the values you get force=239.616 N.

Level 2!!!

Aditya Dutta - 7 years, 2 months ago

It is correct ?

Romms Basa - 6 years, 11 months ago

did not see the 3fms of the nucleus! calculation error

Nibir Das - 6 years, 11 months ago

Formula for coulombic force:

k q 1 q 2 d 2 k\frac{q_1 q_2}{d^2}

where d d is the distance of seperation = ( 2 + 3 ) f m = 5 f m = (2+3) fm = 5 fm

q 1 q_1 is the charge of the pinging proton = 1.60218 × 1 0 19 C = 1.60218 \times10^{-19} C

q 2 q_2 is the charge of the nucleus of iron with 26 protons = 26 × 1.60218 × 1 0 19 C = 26 \times 1.60218 \times10^{-19} C

You get k = 9 × 1 0 9 k = 9 \times 10^9 from the question.

So

( 9 × 1 0 9 ) ( 26 × 1.60218 × 1.60218 ) 1 0 19 × 1 0 19 ( 5 1 0 15 ) 2 = 240.268 \frac{\left(9 \times 10^9\right) (26 \times 1.60218 \times 1.60218)}{10^{19} \times 10^{19} \left(\frac{5}{10^{15}}\right)^2} = \boxed{240.268} is the answer in Newtons

how is the distance of seperation is 5fm

Masood Salik - 6 years, 10 months ago

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You need to consider the distance from the center of the nucleus, not from the surface.

Vishnu Bhagyanath - 5 years, 11 months ago
Rindell Mabunga
Mar 24, 2014

Use Coulumb's Law using 1.60 × 1 0 19 C 1.60 \times 10^{-19} C as the charge of proton and 26 ( 1.60 × 1 0 19 ) C 26(1.60 \times 10^{-19}) C as the charge of the iron nucleus and its distance will be the distance between the proton and the center of the iron nucleus which is 5 f m 5 fm or 5 × 1 0 15 m 5 \times 10^{-15} m

bah! took 3 fm as dia. n 1.5 fm radius, messed up the whole thing, lol

Somesh Singh - 7 years, 2 months ago

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