The breakdown voltage of a pn junction is the voltage at which the reverse-biased electric field across the junction becomes so strong that it causes the depletion region to break down and allows current to flow through the junction. In this case, we are given a uniformly doped silicon pn junction with a dopant profile of Na = Nd = 5 x 1016 cm-3 and a peak electric field at breakdown of E = 4 x 105V/cm.

1. Understanding the breakdown voltage:
The breakdown voltage is determined by the electric field strength across the junction and the width of the depletion region. When the electric field reaches a certain threshold value, called the critical electric field, the junction experiences avalanche breakdown and allows current to flow. The breakdown voltage is given by the equation:
Vbr = Ed * Wd

2. Determining the critical electric field:
The critical electric field for silicon is approximately 3 x 105V/cm. If the peak electric field at breakdown is given as E = 4 x 105V/cm, it exceeds the critical electric field.

3. Determining the width of the depletion region:
The width of the depletion region can be calculated using the formula:
Wd = sqrt(2 * ε * (Vbi + Vr) / (q * (Na + Nd)))

4. Calculating the breakdown voltage:
Substituting the given values into the equation, we can calculate the breakdown voltage:
Vbr = Ed * Wd = (4 x 105V/cm) * Wd

Since the doping concentrations are the same on both sides of the junction, the built-in potential Vbi is zero. Therefore, the equation simplifies to:
Vbr = (4 x 105V/cm) * Wd = (4 x 105V/cm) * sqrt(2 * ε * Vr / (q * Na))

Substituting the values for ε (the permittivity of silicon), Vr (the reverse bias voltage), q (the charge of an electron), and Na (the doping concentration), we can calculate the breakdown voltage.

5. Calculation:
Using the given values, we have:
Vbr = (4 x 105V/cm) * sqrt(2 * 11.8 * 8.854 x 10-14 F/cm * Vr / (1.6 x 10-19 C * 5 x 1016 cm-3))

Simplifying the equation, we find:
Vbr = (4 x 105V/cm) * sqrt(2.14 x 10-3 * Vr)

To calculate the breakdown voltage, we need to know the value of Vr. However, it is not provided in the given information. Without the value of Vr, we cannot accurately calculate the breakdown voltage.

Therefore, without the value of Vr, it is not possible to determine the correct answer option.