(Solved): Alpha particles of kinetic energy \( 5.3 \mathrm{MeV} \) are incident at a ra ...

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Alpha particles of kinetic energy \( 5.3 \mathrm{MeV} \) are incident at a rate of \( 2.9 \times 10^{7} \) per second on an aluminum foil of thickness \( 2.9 \times 10^{-6} \mathrm{~m} \). A circular detector of diameter \( 1.0 \mathrm{~cm} \) is placed \( 13 \mathrm{~cm} \) from the foil at an angle of \( 30^{\circ} \) with the direction of the incident alpha particles. At what rate does the detector measure scattered alpha particles? (The molar mass of aluminum is \( 27.0 \mathrm{~g} / \mathrm{mol}^{2} \) and its density is \( 2.7 \mathrm{~g} / \mathrm{cm}^{3} \).) \[ s^{-1} \]