The next two questions are related to the following situation: A particle of unk

Question

The next two questions are related to the following situation:
A particle of unknown mass is in a 1-dimensional box of width L = 3.0 x 10-10 m with infinitely
high potential walls at x = 0 and at x = L, and zero potential for 0 < x < L. The particle is in the
second excited state of the box.
3. What is the de Broglie wavelength, ?, of the particle?
a. ? = 1.0 x 10-10 m
b. ? = 2.0 x 10-10 m
c. ? = 3.0 x 10-10 m
d. ? = 6.0 x 10-10 m
e. Not enough information is given.


4. For which values of x is the probability of finding the particle largest?
a. Only at x = L/6 and x =5 L/6 (two values of x)
b. Only at x = L/4 (one value of x)
c. Only at x = L/6 and at x = L/2 and at x = 5L/6 (three values of x)
d. The probability is everywhere the same.
e. Not enough information is given.

Explanation / Answer

(3)

= h/p = h 2 L / (h n) = 2 L/n

For second excited state , n=3

=2*3.0 x 10-10/3

=2.0 x 10-10 m

(4)

Probability density function:

  2(x)=(2/L)sin2(nx/L)

d2(x)/dx =2sin(nx/L)cos(nx/L)=0

n=3

   x = L/6

sin(/2)cos(/2)=0

and at x = L/2

  sin(3/2)cos(3/2)=0

and at x = 5L/6

sin(5/2)cos(5/2)=0

c. Only at x = L/6 and at x = L/2 and at x = 5L/6 (three values of x)

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.