Given below are two statements:

Statement I : Davission-Germer experiment establishes, the wave nature of electrons.

Statement II : If electrons have wave nature, they can interfere and show diffraction.

In the light of the above statements choose the correct answer from the option given below:

z² × (13.6) (1 - ¼) = 3 × (13.6)
z = 2 . (i)
h/√2mk? = (1/2.3) × h/√2mk?
=> k? = (2.3)²k? = 5.25k? (ii)
Now, k? = E? - Φ
k? = E? - Φ = z²E? - Φ
∴ k? /k? = (10.2 - Φ)/ (4 × 10.2 - Φ) = 1/5.25
=> Φ = 3eV

 ${}_{}\frac{}{}$ $K.E_1=\frac{1230}{800}-?$ - (i)

${}_{}{}_{}\frac{}{}$  $K.E_2=2K.E_1=\frac{1230}{500}-?$ - (ii)

from (i) & (ii)

$$ $?=0.615$  ev

hu = hu₀ + K.E

Cases u = 2u₀

h2u₀ = hu₀ + K.E₁

K.E₁ = hu₀

$\frac{1}{2}m{v}_1^2=h{\upsilon }_0$

$v_1^2=\frac{2h{\upsilon }_0}{m}$  

$v_1=\sqrt[]{\frac{2h{\upsilon }_0}{m}}$ - (1)      

Now, cases 2

h 5u₀ = hu₀ + k.E₂

k.E₂ = 4hu₀

$\frac{1}{2}m{v}_2^2=4h{\upsilon }_0$

v₂ =     $\sqrt[]{\frac{8h{\upsilon }_0}{m}}$   - (2)

$\frac{v_2}{v_1}=\sqrt[]{\frac{8}{2}=2}$          

v₂ = 2v₁

This is a Short Answer Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}f\left(x\right)=\frac{2x^2-3x-2}{x-2}\\ =\frac{2x^2-4x+x-2}{x-2}=\frac{2x\left(x-2\right)+1\left(x-2\right)}{x-2}\\ =\frac{\left(2x+1\right)\left(x-2\right)}{x-2}=2x+1\\ \underset{x\to 2^{-}}{lim}f\left(x\right)=2x+1=\underset{h\to 0}{lim}2\left(2-h\right)+1=4+1=5\\ \underset{x\to 2^{+}}{lim}f\left(x\right)=2x+1=\underset{h\to 0}{lim}2\left(2+h\right)+1=4+1=5\\ \underset{x\to 2}{lim}f\left(x\right)=5\\ As\underset{x\to 2^{-}}{lim}f\left(x\right)=\underset{x\to 2^{+}}{lim}f\left(x\right)=\underset{x\to 2}{lim}f\left(x\right)=5\\ Hence,f\left(x\right)iscontinuousatx=2.\end{array}$

This is a Short Answer Type Questions as classified in NCERT Exemplar

Explanation- p=100W

_{$\lambda$ 1}= 1nm

_{$\lambda$ 2}= 500nm

Also n₁and n₂ represent number of photon of x-rays and visible light emitted from the two sources per sec

E/t=P=n₁hc/ $\lambda$ ₁₌n₂hc/ $\lambda$ ₂

So n₁/ $\lambda$ ₁ = n₂/ $\lambda$ ₂

So n₁/n₂= 1/500