Semiconductor Electronics Materials Devices And Simple Circuits

1. Given Equation for :
We are given the following equation for :

2. Expression for :
We also have the expression for :

3. Ratio for Same Beam:
For the same beam, the ratio is:

4. Finding the Value of and :
We are given the relationship between and :

5. Final Calculation:
Using the given values and simplifying:

To construct a dimensionless quantity from , , , and , we assign their respective dimensional formulas with powers , , , and . The expression takes the form:

The dimensions of each quantity are:

The dimensionless condition implies:

for the product

Equating powers for each dimension:

1. Mass (M):
(Equation 1)

2. Length (L):
(Equation 2)

3. Time (T):
(Equation 3)

4. Current (I):
(Equation 4)

By solving these equations systematically:

From Equation 4:

Substitute into Equation 3:

(Equation 5)

Use Equation 1:

Substitute in Equation 5:

Hence,

Thus, , , , , as is a non-zero integer.

The tuple is .