Considering Bohr model of atom, for each of the following identify them to be true or false andgive qualitative as well as quantitative explanation for your answer.a. For the same atom, as orbit number increases, the velocity of electron increasesb. For the same orbit number, as atomic number increases, the electron comes closer to thenucleus
Question
Considering Bohr model of atom, for each of the following identify them to be true or false andgive qualitative as well as quantitative explanation for your answer.a. For the same atom, as orbit number increases, the velocity of electron increasesb. For the same orbit number, as atomic number increases, the electron comes closer to thenucleus
Solution
a. False. According to the Bohr model of the atom, as the orbit number (n) increases, the velocity of the electron decreases. This is because the electron is further from the nucleus and therefore experiences less electrostatic attraction. The velocity of an electron in a Bohr orbit is given by the equation v = e^2/(2ε₀hn), where e is the charge of the electron, ε₀ is the permittivity of free space, h is Planck's constant, and n is the orbit number. As n increases, v decreases.
b. True. For the same orbit number, as the atomic number (Z) increases, the electron comes closer to the nucleus. This is because the atomic number is proportional to the nuclear charge, and a greater nuclear charge exerts a stronger electrostatic attraction on the electron, pulling it closer to the nucleus. The radius of a Bohr orbit is given by the equation r = ε₀n²h²/(πmZe²), where m is the electron mass. As Z increases, r decreases, meaning the electron is closer to the nucleus.
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