A4. The ratio of the maximum frequency of a photon in the Balmer series to the minimum frequency in the Paschen series in the spectrum of a hydrogen atom is __ 1. 2,86 2.2.25 3.5,1 4.5,3

The correct answer is 1. $2,86$.<br /><br />The Balmer series in the hydrogen atom spectrum corresponds to the transitions of electrons from higher energy levels to the n=2 energy level. The Paschen series corresponds to transitions from higher energy levels to the n=3 energy level.<br /><br />The maximum frequency in the Balmer series occurs when the electron transitions from the highest possible energy level (n=∞) to the n=2 level. The minimum frequency in the Paschen series occurs when the electron transitions from the n=3 level to the lowest possible energy level (n=1).<br /><br />Using the Rydberg formula for hydrogen, the frequency of a photon emitted during a transition between two energy levels can be calculated as:<br /><br />f = R_H * (1/n1^2 - 1/n2^2)<br /><br />where f is the frequency, R_H is the Rydberg constant, and n1 and n2 are the principal quantum numbers of the two energy levels.<br /><br />For the maximum frequency in the Balmer series (n1=2, n2=∞), the frequency is:<br /><br />f_max = R_H * (1/2^2 - 1/∞^2) = R_H * (1/4 - 0) = R_H/4<br /><br />For the minimum frequency in the Paschen series (n1=3, n2=1), the frequency is:<br /><br />f_min = R_H * (1/3^2 - 1/1^2) = R_H * (1/9 - 1) = -8R_H/9<br /><br />The ratio of the maximum frequency in the Balmer series to the minimum frequency in the Paschen series is:<br /><br />f_max / f_min = (R_H/4) / (-8R_H/9) = -9/32<br /><br />Therefore, the correct answer is 1. $2,86$.