PHY3707 Assignment 5 Solutions 2026
UNISA
Opened: Tuesday, 30 June 2026, 8:00 AM
Due: Tuesday, 11 August 2026, 3:00 PM
Dear PHY3707 Student
Kindly find the attached Assessment 5 with
Unique number 197163.
, Question 1
(a)
Assuming the Drude model, show that the probability for an electron, picked at
random at any time, not to have made a collision during the preceding time 𝑡is
𝑃(𝑡) = 𝑒 −𝑡/𝜏
where 𝜏 is the mean free time between collisions.
Solution
Define the probability
Let
𝑃(𝑡)
be the probability that an electron has not suffered a collision during the previous time
interval 𝑡.
According to the Drude model:
• Every collision is completely random.
• The probability of collision per unit time is constant.
• The average time between collisions is
𝜏
Therefore, the probability of a collision occurring in a very small time interval 𝑑𝑡is
𝑑𝑡
.
𝜏
Hence, the probability that no collision occurs during 𝑑𝑡is
𝑑𝑡
1− .
𝜏
Write the probability after an additional time 𝒅𝒕
UNISA
Opened: Tuesday, 30 June 2026, 8:00 AM
Due: Tuesday, 11 August 2026, 3:00 PM
Dear PHY3707 Student
Kindly find the attached Assessment 5 with
Unique number 197163.
, Question 1
(a)
Assuming the Drude model, show that the probability for an electron, picked at
random at any time, not to have made a collision during the preceding time 𝑡is
𝑃(𝑡) = 𝑒 −𝑡/𝜏
where 𝜏 is the mean free time between collisions.
Solution
Define the probability
Let
𝑃(𝑡)
be the probability that an electron has not suffered a collision during the previous time
interval 𝑡.
According to the Drude model:
• Every collision is completely random.
• The probability of collision per unit time is constant.
• The average time between collisions is
𝜏
Therefore, the probability of a collision occurring in a very small time interval 𝑑𝑡is
𝑑𝑡
.
𝜏
Hence, the probability that no collision occurs during 𝑑𝑡is
𝑑𝑡
1− .
𝜏
Write the probability after an additional time 𝒅𝒕
