A lithium nucleus with a charge of 3(1.6 × 10^-¹⁹)C and a mass of 7(1.67 × 10^-²⁷)kg,and an alpha particle with a charge of 2(1.6 × 10^-¹⁹)C and a mass of 4(1.67 × 10^-²⁷)kg,are at rest.They could be accelerated to the same kinetic energy by A)accelerating them through the same electrical potential difference. B)accelerating the alpha particle through V volts and the lithium nucleus through 2V/3 volts. C)accelerating the alpha particle through V volts and the lithium nucleus through 7V/4 volts. D)accelerating the alpha particle through V volts and the lithium nucleus through 7V/6 volts. E)none of these procedures

Question

Quizplus · Accepted Answer

The kinetic energy of a particle with charge q and mass m accelerated through a potential difference V can be given as:
K = qV/2m
Both the lithium nucleus and alpha particle need to have the same kinetic energy, hence:
q_Li*V_Li/2m_Li = q_alpha*V_alpha/2m_alpha
Substituting the values given in the question:
3(1.6 × 10^-19) V_Li/ (2*7(1.67 × 10^-27)) = 2(1.6 × 10^-19) V_alpha/ (2*4(1.67 × 10^-27))
Simplifying, we get:
V_Li = (2/3)V_alpha
Hence, the alpha particle needs to be accelerated through V volts and the lithium nucleus needs to be accelerated through 2V/3 volts to have the same kinetic energy. Therefore, the best choice is B.

A Lithium Nucleus with a Charge of 3(1