Question

A electric beam is incident on a potential barrier at height 0.03ev and of infinite with find the reflection coefficient of the barrier if the energy of the incident electric beam be (a)0.04ev(b)0.025ev(c)0.03ev.

Answer 1

GIVEN:

$V_o=0.03eV \\a) E_1=0.04\\b)E_2=0.025\\c)E_3=0.03$

first we find the transmission coefficient (T) for the step like potential:

$\boxed{T={4\sqrt E \sqrt{E-V_o}\over (\sqrt E + \sqrt{E-V_o})^2}}$ ............1

then reflection coefficient (R).

$\boxed{R=1-T}$ ...............................2

now using 1 and 2 we calculate $T_1,T_2,T_3$ AND $R_1,R_2,R_3$

a)

$\boxed{T_1={4\sqrt 0.04 \sqrt{0.04-0.03}\over (\sqrt0.04 + \sqrt{0.04-0.03})^2}=0.889} \\$

$\boxed{R_1=1-T=0.111}$

b)

$\boxed{T_2={4\sqrt 0.025 \sqrt{0.025-0.03}\over (\sqrt0.025 + \sqrt{0.025-0.03})^2}=error} \\$ no value exists because ,E<V and squre root is not defined for negative value.

therefore, value of $R_2=$ not defined

c)

$\boxed{T_3={4\sqrt 0.03 \sqrt{0.03-0.03}\over (\sqrt0.03 + \sqrt{0.03-0.03})^2}=0}$

therefore

$\boxed{R_3=1-0=1}$