An \( \alpha \) particle is scattered from an Au target at rest as shown in the figure. \( D_1 \) and \( D_2 \) are the detectors to detect the scattered \( \alpha \) particle at an angle \( \theta \) and along the beam direction, respectively, as shown. The signals from \( D_1 \) and \( D_2 \) are converted to logic signals and fed to logic gates. When a particle is detected, the signal is 1 and is 0 otherwise. Which one of the following circuits detects the particle scattered at the angle \( \theta \) only?
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In cases where simultaneous detection from multiple sources is required, use the AND gate configuration.
Logic gates with \( D_1 \) and \( D_2 \) in AND configuration.
Logic gates with \( D_1 \) and \( D_2 \) in OR configuration.
Logic gates with \( D_1 \) in AND and \( D_2 \) in NOT configuration.
Logic gates with \( D_1 \) in OR and \( D_2 \) in NOT configuration.
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The Correct Option isA
Solution and Explanation
Step 1: The logic gates are used to detect the particle that is scattered at angle \( \theta \) only. For this, the signal from both detectors \( D_1 \) and \( D_2 \) need to be simultaneously 1, which occurs when both detectors register a signal. This can be done using the AND gate logic. Step 2: In the AND configuration, both \( D_1 \) and \( D_2 \) must detect the particle for the output to be 1, which corresponds to the particle being scattered at the desired angle \( \theta \). If either of the detectors does not register the particle, the output will be 0.
