particle in a box

For a particle in a box, the PE inside the box is taken as

• infinity

• zero

• finite

• can't say anything

The expectation value of momentum of a paricle inside a box is

• zero

• $\pm\frac{nh}{2L}$

• $\pm\frac{n\pi h}{2L}$

• $+\frac{n\pi h}{2L}$

• $-\frac{n\pi h}{2L}$

The wavefunction of a particle in a box is given by

 $\Psi=A\sin\ \frac{n\pi x}{L}$  where A =

•  $\sqrt{\frac{2}{L}}$  

•  $\sqrt{\frac{L}{2}}$  

•  $\sqrt{\frac{2L}{h}}$  

•  $\sqrt{\frac{2h}{L}}$  

The first excited state energy of an electron in a box of 1Å width

• 130.5 eV

• 140.5 eV

• 150.5 eV

• 160.5 eV

The expectation value of position of a particle trapped in a box of width L is

• 0

• L

• $\frac{L}{2}$

• $\frac{L}{4}$

The probability of finding the particle on a box of width L, at x = L is

• 1

• 0

• 0.5

• 0.75

The eigen value of momentum of a particle in a box is

• 0

• $\pm\frac{nh\pi}{L}$

• $\pm\frac{nh}{2L}$

• $\pm\frac{n\pi}{2hL}$

The eigen value obtained when the operator

 $\frac{d^2}{dx^2}$  operates on the eigen function 'sin x' is

• cos x

• 0

•  $+1$  

•  $-1$  

Does the energy of a free paricle in a box depend on width of the box

• yes

• no

which are the positions at which the wavefunction of a particle in a box becomes zero in the second excited state?

• 0, L

• $0,\ \frac{L}{2},\ L$

• $0,\ \frac{L}{3},\ \frac{2L}{3},\ L$

• $0,\ \frac{L}{4},\ \frac{3L}{4},\ L$