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We know that in the Bohr model, angular momentum is quantised as $L= n\hbar = nh/(2\pi)$. So when an electron jumps from one state to another, its angular momentum certainly changes, which means that a torque must be acting on the electron. Our consideration in resolving the Bohr model were the electrostatic forces, which act radially, and cannot generate torque. My question is, where does that torque come from?

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As with all questions about the Bohr model that are quantitative about anything other than the energy levels, the answer is: don't use the Bohr model. It's been superseded by quantum mechanics and its predictions are only of historical interest.

However, within the Bohr model, the electron's orbit is due to electrostatic forces, but the transitions are caused by external electromagnetic fields which are not constrained to act radially, so there is no contradiction at all.

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When $l$ changes, the angular momentum is carried away by the emitted photon.

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