**Problem 3:**(a) Consider an object of constant mass \( m \) acted on by a three-force \( \mathbf{F} \). According to special relativity, prove that \( \mathbf{F} = \gamma m \mathbf{a} + (\mathbf{F} \cdot \mathbf{v}) \mathbf{v}/c^2 \). Hint: Compute \( \frac{dE}{dt} \) to notice that it appears in \( \frac{dp}{dt} \), and show that \( \frac{dE}{dt} = \mathbf{F} \cdot \mathbf{v} \).(b) In a hot star, a multiply-ionized, hydrogen-like atom with a single remaining electron produces a series of spectral lines as described by the Bohr model. The series corresponds to electronic transitions that terminate in the same final state. The longest and shortest wavelengths of the series are 63.3 nm and 22.8 nm, respectively. What is the ion?

Given F = γ ma + F.v vc2 λlongest = 63.3 nmλshortest = 22.8 nm

Answered: Problem 3: (a) Consider an object of…

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