To compute the smallest radius of a hydrogen atom, we use the Bohr model formula for the radius of an electron orbit. The problem provides values for Planck's constant (h), mass of electron (m_e),
This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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To compute the smallest radius of a hydrogen atom, we use the Bohr model formula for the radius of an electron orbit. The problem provides values for Planck's constant ($h$), mass of electron ($m_e$), and electron charge ($e$). It also specifies $Z=1$ for hydrogen and $n=1$ for the smallest radius (ground state).
The given value for the electron charge, $e = 4.80 \times 10^{-10} \, \text{C}$, is unusual for SI units. This value is actually the magnitude of the electron charge in electrostatic units (esu) in the CGS system. To obtain a physically reasonable result (the Bohr radius), it is necessary to assume that the problem intends for this value of $e$ to be used
