The energy of electron in an atom is given by En =
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according to Bohr's theory ,
angular momentum = nh/2π
mvr = nh/2π ------(1)
Also centripetal force = Electrostatic force
mv²/r = KZe²/r²
mvr = KZe²/v -----(2)
From equations (1) and (2),
KZe²/rv = nh/2π
v = KZe²2π/nh
in C.G.S system, K = 1
so, v = 2πZe²/nh
Now, kinetic energy = 1/2 mv² = 1/2 m × 4π²Z²e⁴/n²h²
= 2π²Z²e⁴m/n²h²
we also know, total energy = - kinetic energy
So, En = - 2π²Z²e⁴m/n²h²
If hydrogen atom is taken then Z = 1
now, En = -2π²e⁴m/n²h²
Hence, option (c) is correct
angular momentum = nh/2π
mvr = nh/2π ------(1)
Also centripetal force = Electrostatic force
mv²/r = KZe²/r²
mvr = KZe²/v -----(2)
From equations (1) and (2),
KZe²/rv = nh/2π
v = KZe²2π/nh
in C.G.S system, K = 1
so, v = 2πZe²/nh
Now, kinetic energy = 1/2 mv² = 1/2 m × 4π²Z²e⁴/n²h²
= 2π²Z²e⁴m/n²h²
we also know, total energy = - kinetic energy
So, En = - 2π²Z²e⁴m/n²h²
If hydrogen atom is taken then Z = 1
now, En = -2π²e⁴m/n²h²
Hence, option (c) is correct
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