Principle: Diffraction effects are observed for beams of electrons scattered by the crystals.
λ = \(\frac { h }{ p } =\frac { h }{ \sqrt { 2mE_{ k } } } =\frac { h }{ \sqrt { 2meV } } \)
= \(\frac { 6.63\times { 10 }^{ -34 } }{ \sqrt { 2\times 9.1\times 10^{ -31 }\times 1.6\times 10^{ -19 }\times 120 } } \)
λ = 0.112 nm.

In ground state, the kinetic energy of the electron is
K = -E =  \(\frac { +13.6eV }{ 1^{ 2 } } \) =13.6 x 1.6 x 10^-19 J
de Broglie wavelength,
λ  = \(\frac { h }{ p } =\frac { h }{ \sqrt { 2mK } } \)
λ₁ = -\(\frac { 6.63\times { 10 }^{ -34 } }{ \sqrt { 2\times 9.1\times 10^{ -31 }\times 2.18\times 10^{ -18 } } } \)
= 9.33 x 10^-9 = 0.33 nm
Kinetic energy in the first excited state (n = 2)
K = -E = + \(\frac { 13.6 }{ 2^{ 2 } } \) eV = +3.4 eV
= 3.4 x 1.6 x 10^-19 J
= 0.54 x 10^-18 J
de Broglie wavelength,
λ₂ = \(\frac { h }{ \sqrt { 2mK } } \)
=  \(\frac { 6.63\times { 10 }^{ -34 } }{ \sqrt { 2\times 9.1\times { 10 }^{ -31 }\times 0.544\times { 10 }^{ -15 } } } \)
= 2 x 0.33 nm = 0.66 mm.

(i) The threshold frequency is the frequency of incident light at which kinetic energy of ejected photoelectron is zero.
∴ From fig. threshold frequency,
v₀ = 4.5 x 10¹⁴ Hz
(ii) Work function, W = hv₀
= 6.6 x 10^-34 x 4.5 x 10¹⁴ joule
= \(\frac { 6.6\times { 10 }^{ -34 }\times 4.5\times 10^{ 14 } }{ 1.6\times { 10 }^{ -19 } } \) eV
= 1.85 eV

X-rays are being used in many fields. Let us list a few of them.
(i) Medical diagnosis X-rays can pass through flesh more easily than through bones. Thus an x-ray radiograph containing a deep shadow of the bones and a light shadow of the flesh may be obtained. X-ray radiographs are used to detect fractures, foreign bodies, diseased organs, etc.
(ii) Medical therapy Since x-rays can kill diseased tissues, they are employed to cure skin diseases, malignant tumors, etc.
(iii) Industry X-rays are used to check for flaws in welded joints, motor tires, tennis balls, and wood. At the customs post, they are used for the detection of contraband goods.
(iv) Scientific research X-ray diffraction is an important tool to study the structure of the crystalline materials - that is, the arrangement of atoms and molecules in crystals.

Energy differnce = Energy of emitted photon
= E₂ - E₁
= -1.51 - (-3.4) = 1.89 eV
= 1.89 x 1.6 x 10^-19 J
λ = \(\\ \frac { hc }{ { E }_{ 2 }-{ E }_{ 1 } } \)
= \(\frac { 6.6\times { 10 }^{ -34 }\times 3\times { 10 }^{ 8 } }{ 1.89\times 1.6\times 10^{ -19 } } =\frac { 19.8 }{ 3.024 } \) x 10^-7
= 6.548 x 10^-7 m = 6548 Å
The wavelength belongs to the Balmer series of the hydrogen spectrum.