Explanation Given Info : Copper atoms have 29 protons in their nuclei and the copper nucleus is taken as a sphere with a diameter of 4.8 × 10 − 15 m . The charge on the alpha particle is equal to + 2 e . The nucleus of copper is a sphere. Alpha particle is present at rest at infinity. To bring this alpha particle from rest at infinity to the surface of the nucleus, certain amount of work is required. Therefore, the amount of work required to bring an alpha particle from rest at infinity to the surface of the nucleus is equal to the potential energy possessed by the alpha particle. The formula to calculate the net amount of work is, W = V × q (1) Here, W is the amount of work. V is the electrical potential. q is the charge present on alpha particle. The electrical potential used in above formula is to be calculated. Copper atoms comprises of 29 protons. Therefore, the charge present on copper nucleus is equal to 29 e . The diameter of copper nucleus is 4.8 × 10 − 15 m . The formula to calculate the radius of copper nucleus is, Radius = Diameter 2 Substitute, 4.8 × 10 − 15 m for diameter to find radius of the copper nucleus. Radius = Diameter 2 = 4.8 × 10 − 15 m 2 = 2.4 × 10 − 15 m Thus, the calculated value of radius of copper nucleus is 2.4 × 10 − 15 m . The formula to calculate the electrical potential is, V = k × Q r Here, k is the proportionality constant and is equal to 9 × 10 9 Nm 2 /C 2 . Q is the charge present on copper nucleus and is equal to 29 e . r is the radius of copper nucleus and is equal to 2.4 × 10 − 15 m . Substitute, 9 × 10 9 Nm 2 /C 2 for k , 29 e for Q , 2.4 × 10 − 15 m for r to find electrical potential of the copper nucleus. V = k × Q r = 9 × 10 9 Nm 2 /C 2 × 29 e 2

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Chapter 31, Problem 4PCE

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The amount of work required to bring an alpha particle (charge =+2 e ) from rest at infinity to the “surface” of the nucleus.

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The amount of work required to bring an alpha particle (charge = + 2 e ) from rest at infinity to the “surface” of the nucleus.

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The amount of work required to bring an alpha particle (charge =+2 e ) from rest at infinity to the “surface” of the nucleus.

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