Question
The radionuclide $^{11}C$ decays according to
$^{11}_{6}\text{C}\rightarrow^{11}_{5}\text{B}+\text{e}^{+}+\text{v}:\ \text{T}_{1/2}=20.3 \text{ min}$
The maximum energy of the emitted positron is 0.960 MeV.
Given the mass values:
$\text{m}(^{11}_{6})=10=11.011434\text{ u and m}(^{11}_{6}\text{B})=11.009305\text {u}.$
calculate Q and compare it with the maximum energy of the positron emitted.

Answer

For the given reaction, mass defect is,
$\Delta\text{m}=[\text{m}(^{11}_{6}-6\text{m}_\text{e})]-[\text{m}(^{11}_{5}\text{B})-5\text{ m}_\text{e}+\text{m}_\text{e}]$
$=\text{m}(^{11}_{6}\text{C})-\text{m}(^{11}_{5}\text{B})-2\text{m}_\text{e}$
$= 11.011434\ u -11.009305\ u - 2 × 0.000548\ u$
$= 0.001033$ u
Now, Q-value is,
$Q = 0.001033 × 931.5$ MeV
$= 0.962$ MeV
which, is the maximum energy of the positron.
We have,
$\text{Q}=\text{E}_\text{d}+\text{E}_\text{e}+\text{E}_\text{v}$
The daughter nucleus is too heavy compared to $e^+$ and v. So, it carries negligible energy $(\text{E}_\text{d}\approx0).$ If the kinetic energy $(E_v)$ carried by the neutrino is minimum (i.e., zero), the positron carries maximum energy, and this is practically all energy Q.
Hence, maximum $\text{E}_\text{e}\approx\text{Q}.$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

How many time constants will elapse before the power delivered by a battery drops to half of its maximum value in an RC circuit?
A 0.5m long metal rod PQ completes the circuit as shown in the figure. The area of the circuit is perpendicular to the magnetic field of flux density 0.15T. If the resistance of the total circuit is $3\Omega$ calculate the force needed to move the rod in the direction as indicated with a constant speed of $2ms^{-1}.$
A monochromatic light of wavelength $\lambda$ is incident normally on a narrow slit of width ‘a’ to produce a diffraction pattern on the screen placed at a distance D from the slit. With the help of a relevant diagram, deduce the conditions for obtaining maxima and minima on the screen. Use these conditions to show that angular width of central maximum is twice the angular width of secondary maximum.
Mention the important considerations required while fabricating a p-n junction diode to be used as a Light Emitting Diode (LED). What should be the order of band gap of an LED if it is required to emit light in the visible range?
An average emf of 20V is induced in an inductor when the current in it is changed from 2.5A in one direction to the same value in the opposite direction in 0.1s. Find the self-inductance of the inductor.
Consider the fusion in helium plasma. Find the temperature at which the average thermal energy 1.5kT equals the Coulomb potential energy at 2fm.
Consider a sphere of radius R with charge density distributed as$\rho\text{(r)}=\text{kr for r}\leq\text{R}$
$=0\text{ for f}>\text{R}.$
Find the electric field at all points r.
A hypothetical magnetic field existing in a region is given by $\overrightarrow{\text{B}}=\text{B}_0\overrightarrow{\text{e}}_\text{r},$ where $\overrightarrow{\text{e}}_\text{r}$ denotes the unit vector along the radial direction. A circular loop of radius a, carrying a current i, is placed with its plane parallel to the x-y plane and the centre at (0, 0, d). Find the magnitude of the magnetic force acting on the loop.
How electromagnetic waves are produced? What is the source of the energy accompanied by any propagating electromagnetic wave?
(i) In far switches of household electrical appliances
(ii) In medical diagnosis
When a photon is emitted from an atom, the atom recoils. The kinetic energy of recoil and the energy of the photon come from the difference in energies between the states involved in the transition. Suppose, a hydrogen atom changes its state from n = 3 to n = 2. Calculate the fractional change in the wavelength of light emitted, due to the recoil.