Atomic StructurehardNUMERICAL

The mass of a moving electron varies with its velocity according to the relation , where is its restAtomic Structure Chemistry Question

Question

The mass of a moving electron varies with its velocity $v$ according to the relation $m = \frac{m_0}{\sqrt{1 - (v/c)^2}}$, where $m_0$ is its rest mass and $c$ is the speed of light. If an electron is accelerated to a velocity of $v = \frac{\sqrt{3}}{2}c$, calculate the ratio of its dynamic mass to its rest mass ($m/m_0$).

Answer: 2

💡 Solution & Explanation

According to the relativistic mass formula, $m = \frac{m_0}{\sqrt{1 - (\frac{\sqrt{3}c}{2c})^2}} = \frac{m_0}{\sqrt{1 - \frac{3}{4}}} = \frac{m_0}{\sqrt{1/4}} = \frac{m_0}{1/2} = 2m_0$. Thus, $m/m_0 = 2$. [18, 19]

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