In \(\beta^-\) decay, a neutron in the nucleus decays into a proton, an electron (\(\beta^-\) particle), and an antineutrino. The electron is emitted from the nucleus, which results in the conversion of the neutron into a proton. The process can be written as: \[ n \rightarrow p + e^- + \overline{\nu}_e \] Thus, during \(\beta^-\) decay, a neutron in the nucleus decays emitting an electron, which is the characteristic feature of this type of radioactive decay.
The correct answer is (C) : A neutron in the nucleus decays emitting an electron.
In \( \beta^- \) decay, a neutron in the nucleus decays into a proton, emitting an electron (also called a beta particle) and an antineutrino. This is the fundamental process in \( \beta^- \) decay.
The reaction is as follows:
\(n \rightarrow p + e^- + \bar{\nu}_e\)
Where:
- \( n \) is the neutron,
- \( p \) is the proton,
- \( e^- \) is the emitted electron (beta particle),
- \( \bar{\nu}_e \) is the emitted antineutrino.
The key point here is that the neutron decays into a proton while emitting an electron (and an antineutrino) in the process. This distinguishes \( \beta^- \) decay from other processes like \( \beta^+ \) decay, where a proton decays into a neutron.
Therefore, the correct answer is (C) — A neutron in the nucleus decays emitting an electron.
A small bob A of mass m is attached to a massless rigid rod of length 1 m pivoted at point P and kept at an angle of 60° with vertical. At 1 m below P, bob B is kept on a smooth surface. If bob B just manages to complete the circular path of radius R after being hit elastically by A, then radius R is_______ m :
Match the following:
In the following, \( [x] \) denotes the greatest integer less than or equal to \( x \). 
Choose the correct answer from the options given below:
For x < 0:
f(x) = ex + ax
For x ≥ 0:
f(x) = b(x - 1)2