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**Question 1: Energy of an electron is given by E = -2.178×10 ^{-18} J Z^{2}/n^{2}. Wavelength of light required to excite an electron in an hydrogen atom from level n =1 to n = 2 will be (h = 6.62 ×10^{−34 }Js and c = 3.0 ×10^{8 }ms^{−1}) (IIT JEE-2013)**

We know that energy of an electron can be calculated using Planck relation

E = hc/λ …………… (i)

But in the question it is given that

E = -2.178 × 10

On comparing both the equations we get,

hc /λ =-2.178×10

On substituting the values

h =6.62 ×10

c = 3.0 ×10

n

In equation (iii) and calculating for the value of λ we get,

λ =1.214 ×10

Hence, the correct option is d.

According to Bohr’s postulate,

Electrons can exist only in those orbital around the nucleus, for which the angular momentum is integral multiple of h/2π i.e.

mvr = n h/2π

or,

v = n h/2πmr

So, Kinetic Energy of electrons = ½ m (n h/2πmr)

Radius of the orbital i.e. r

For, n=2 & z =1

r = 4 a

So,

Kinetic Energy of electrons = ½ m [4 h

Hence, the correct option is c.

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