Intro to Biological Physics, final exam: solutions
Problem (1) Molecular Interactions
(10 points)
(a)
U(r)
12
Urepulsive = A(r0/r)
U(r
U(r) = 0
req
)=0
r
U(req)
4
Uattractive = B(r0/r)
(3 pts)
(b) U(r) = 0 at
(i) r =
r
(ii) A 0
r
12
r
= B 0
r
4
8
B
Intro to Biological Physics, midterm exam 2: solutions
Problem (1)
(20 points)
A connection between the diffusion constant, D, and the physical volume (of spherical
4 3
k BT
R . Hence,
particles) is given by the Rayleigh equation R =
with V =
3
6 D
4.1 1
Intro to Biological Physics, midterm exam 1: solutions
Problem (1)
(20 points)
(a) Binding energy in vacuum: Use known value of Bjerrum length to ease up calculate.
However, remember lB = 7 is valid in water ( = 80)!
1 e2
e2
U=
; lB =
= 7 (for = 80)
4 0
r
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Homework 4 (due October 18, 2012)
(1) Gaussian Distribution
(15 pts)
A random variable x has a Gaussian distribution around its mean, x0:
1
e
2
P( x ) =
( x x 0 )2
2 2
.
2
, show that var( x ) = x 2 x0 = 2.
2
b) Consider two Gaussian distributions, P1(x)
Introduction to Biological Physics: InClass Exam 1 October 20, 2011
your name goes here
This exam has 4 problems on 4 separate pages (total no. of pages: 5). Total available processing time: 80 min.
Read the problem statements carefully! Be sure to under
Introduction to Biological Physics: InClass Exam 2 November 22, 2011
your name goes here
This exam has 4 problems on 4 separate pages (total no. of pages: 6). Total available processing time: 80 min.
Read the problem statements carefully! Be sure to unde
Intro to Biological Physics, midterm exam 1: solutions
Problem (1)
(20 points)
(a) Binding energy in vacuum: Use known value of Bjerrum length to ease up calculate.
However, remember lB = 7 is valid in water ( = 80)!
1 e2
e2
U=
; lB =
= 7 (for = 80)
4 0
Intro to Biological Physics, midterm exam 2: solutions
Problem (1)
(20 points)
A connection between the diffusion constant, D, and the physical volume (of spherical
4 3
k BT
R . Hence,
particles) is given by the Rayleigh equation R =
with V =
3
6 D
4.1 1
Intro to Biological Physics, final exam: solutions
Problem (1) Molecular Interactions
(10 points)
(a)
U(r)
12
Urepulsive = A(r0/r)
U(r
U(r) = 0
req
)=0
r
U(req)
4
Uattractive = B(r0/r)
(3 pts)
(b) U(r) = 0 at
(i) r =
r
(ii) A 0
r
12
r
= B 0
r
4
8
B