In the Thomson model of hydrogen atom, the nuclear charge is distributed uniformly over a sphere of radius 𝑅. The average potential energy of an electron confined within this atom can be taken as $V=\frac{e^2}{4{\pi}e_0R}$ . Taking the uncertainty in position to be the radius of the atom, the minimum value of 𝑅 for which an electron will be confined within the atom is estimated to be 𝑓 × 10 −11 m. The value of 𝑓 is _______ (rounded off to one decimal place). Given: The uncertainty product of momentum and position is ℏ = 1×10 −34 Js -1 ,e=1.6 × 10 −19 C, and $\frac{1}{4{\pi}e_0}$ = 9 × 10 9 Nm2C −2

Question

In the Thomson model of hydrogen atom, the nuclear charge is distributed uniformly over a sphere of radius 𝑅. The average potential energy of an electron confined within this atom can be taken as $V=\frac{e^2}{4{\pi}e_0R}$  . Taking the uncertainty in position to be the radius of the atom, the minimum value of 𝑅 for which an electron will be confined within the atom is estimated to be 𝑓 × 10 −11 m. The value of 𝑓 is _______ (rounded off to one decimal place).  Given: The uncertainty product of momentum and position is ℏ = 1×10 −34 Js -1 ,e=1.6 × 10 −19 C, and  $\frac{1}{4{\pi}e_0}$ = 9 × 10 9 Nm2C −2

cdquestions Admin · Accepted Answer

The correct answer is: 2.2 to 2.7 (approx)

Correct Answer: 2.2 - 2.7

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