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JEE Main 202427 JanuaryEvening Shift
Exam
JEE Main
Year
2024
Date
27 January
Shift
Evening Shift
Subject
Physics
Chapter
Electrostatics

JEE Main 2024 · 27 January · Evening Shift · Physics · Electrostatics

The electric potential at the surface of an atomic nucleus ( Z = 50...

The electric potential at the surface of an atomic nucleus (Z=50)( Z = 50 ) of radius 9×10−13cm9 \times {10}^{- 13}cm is α×106V\alpha \times {10}^{6}V. What is the value of α\alpha?

(Charge of proton 1.6×10−19C1 . 6 \times {10}^{- 19}C)

Correct answer

0

Step-by-step solution

The electric potential at the surface of an atomic nucleus can be written as

V=kQR=k⋅(Ze)R...(1)V = \dfrac{kQ}{R} = \dfrac{k \cdot \left(Ze\right)}{R} . . . \left(1\right)

From equation (1), it follows that

{V=9×109×50×1.6×10−199×10−13×10−2V=8×106V\begin{cases}V & = & \dfrac{9 \times {10}^{9} \times 50 \times 1 . 6 \times {10}^{- 19}}{9 \times {10}^{- 13} \times {10}^{- 2}}V \\ & = & 8 \times {10}^{6}V\end{cases}

Hence, α=8\alpha = 8.

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