pl anser these questions with explanations. very urgent rates are sure

Answer Q-1 and Q-2 based on the information below.
Just like mass and charge, each particle has a quantity called “Lepton Number”. The table below gives charge and Lepton number of some particles. Like charge, lepton number should be conserved in any physical process.
Particle
charge
Lepton number
Proton , p
+e
0
Neutron, n
0
0
Electron, e-
-e
+1
Positron, e+
+e
-1
Neutrino,
0
+1
Antineutrino, bar
0
-1
Q1. The Lepton number of 14C (Z=6, N=8) is

Q-2 Which of the following processes is possible on the basis of conservation laws?
(a) P+e-+ → n (b) p →e+ + (c) p+e- →n + bar (d) p + e- →n +

Let's dive into your questions regarding lepton numbers and particle interactions. Understanding these concepts is crucial in particle physics, especially when discussing conservation laws. We'll tackle each question step by step.

Understanding Lepton Number

Lepton number is a quantum number that helps us keep track of leptons in a system. Each particle has a specific lepton number: electrons and neutrinos have a lepton number of +1, while positrons and antineutrinos have a lepton number of -1. Other particles, like protons and neutrons, have a lepton number of 0. The conservation of lepton number states that in any interaction, the total lepton number before the interaction must equal the total lepton number after the interaction.

Question 1: Lepton Number of 14C

To find the lepton number of carbon-14 (14C), we need to consider its constituents. Carbon-14 has 6 protons (Z=6) and 8 neutrons (N=8). Since protons and neutrons have a lepton number of 0, we focus on the lepton contributions from any electrons or neutrinos present in the system. In its most stable form, 14C does not contain any additional leptons, so:

• Lepton number from protons = 6 * 0 = 0
• Lepton number from neutrons = 8 * 0 = 0
• Total lepton number = 0

Thus, the lepton number of 14C is 0.

Question 2: Possible Processes Based on Conservation Laws

Now, let's analyze the given processes to determine which ones conserve lepton number. We will calculate the total lepton number for each reaction and see if it remains constant.

• (a) P + e- → n
  - Initial lepton number: Proton (0) + Electron (-1) = -1
  - Final lepton number: Neutron (0) = 0
  - Total lepton number changes from -1 to 0, so this process is not allowed.
• (b) p → e+ +
  - Initial lepton number: Proton (0) = 0
  - Final lepton number: Positron (+1) = +1
  - Total lepton number changes from 0 to +1, so this process is not allowed.
• (c) p + e- → n + bar
  - Initial lepton number: Proton (0) + Electron (-1) = -1
  - Final lepton number: Neutron (0) + Antineutrino (-1) = -1
  - Total lepton number remains -1, so this process is allowed.
• (d) p + e- → n +
  - Initial lepton number: Proton (0) + Electron (-1) = -1
  - Final lepton number: Neutron (0) + (unknown particle) = ?
  - Since we don't know the lepton number of the unknown particle, we cannot definitively say this process is allowed or not without more information.

In summary, the lepton number of 14C is 0, and among the processes analyzed, only process (c) is allowed based on the conservation of lepton number. If you have any further questions or need clarification on any points, feel free to ask!