Explain the $\alpha -$ decay process and give its appropriate example
Explain the $\alpha -$ decay process and give its appropriate example
In the $\alpha$-decay phenomenon the unstable nucleus automatically converts and forms a new nucleus and emits $\alpha$-particles.
$\alpha$-particle is the nucleus of helium.
$\therefore \alpha={ }_{2} \mathrm{He}^{4}$
The disintegrating nucleus is called the parent nucleus and the newly formed nucleus is called the daughter nucleus.
In a $\alpha$-decay, the mass number of the product nucleus is four less than that of decaying nucleus
while the atomic number decreases by two.
The equation of $\alpha$-decay can be expressed as follows:
${ }_{\mathrm{Z}}^{\mathrm{A}} \mathrm{X} \rightarrow{ }_{\mathrm{Z}-2}^{\mathrm{A}-4} \mathrm{Y}+{ }_{2}^{4} \mathrm{He}+\mathrm{Q}$
$\text { where } X=\text { parent nucleus }$ $Y=\text { daughter nucleus }$
$Q=$Which is the total kinetic energy released in the process which can be determined from the relation of the mass and energy of the Einstein.
$\mathrm{Q}=\left[m_{\mathrm{X}}-m_{\mathrm{Y}}-m_{\mathrm{He}}\right] c^{2}$
where $m_{\mathrm{X}}=$ mass of parent nucleus
$m_{\mathrm{Y}}=$ mass of daughter nucleus
$m_{\mathrm{He}}=$ mass of $\alpha$-particle and
$c$ speed of light in vacuum
If original nucleus is at rest, $Q$ is the kinetic energy of the products.
As $Q>0$ for $\alpha$-decay, this process is exothermic process as a $Q<0$, this process is endothermic process.
If original nucleus is at rest, $\mathrm{Q}$ is the kinetic energy of the products.
As $\mathrm{Q}>0$ for $\alpha$-decay, this process is exothermic process as a $\mathrm{Q}<0$, this process is endothermic
process.
Example : The decay of ${ }_{92}^{238} \mathrm{U}$ to thorium ${ }_{90}^{234} \mathrm{Th}$ with emission of a helium nucleus ${ }_{2}^{4} \mathrm{He}$
( $\alpha$-particles) whose chemical equation,
${ }_{92}^{238} \mathrm{U} \rightarrow{ }_{90}^{234} \mathrm{~T} h+{ }_{2}^{4} \mathrm{H} e+\mathrm{Q}$
where $\mathrm{Q}$ is the emitted heat,
$\mathrm{Q}=\left[m_{\mathrm{U}}-m_{\mathrm{Th}}-m_{\mathrm{He}}\right] c^{2}$
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Match List $I$ (Wavelength range of electromagnetic spectrum) with List $II$ (Method of production of these waves) and select the correct option from the options given below the lists
List $I$
List $II$
$(1)$ $700\, nm$ to $1\,mm$
$(i)$ Vibration of atoms and molecules
$(2)$ $1\,nm$ to $400\, nm$
$(ii)$ Inner shell electrons in atoms moving from one energy level to a lower level
$(3)$ $ < 10^{-3}\,nm$
$(iii)$ Radioactive decay of the nucleus
$(4)$ $1\,mm$ to $0.1\,m$
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Match List $I$ (Wavelength range of electromagnetic spectrum) with List $II$ (Method of production of these waves) and select the correct option from the options given below the lists
| List $I$ | List $II$ |
| $(1)$ $700\, nm$ to $1\,mm$ | $(i)$ Vibration of atoms and molecules |
| $(2)$ $1\,nm$ to $400\, nm$ | $(ii)$ Inner shell electrons in atoms moving from one energy level to a lower level |
| $(3)$ $ < 10^{-3}\,nm$ | $(iii)$ Radioactive decay of the nucleus |
| $(4)$ $1\,mm$ to $0.1\,m$ | $(iv)$ Magnetron valve |
- [JEE MAIN 2014]
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After absorbing a slowly moving neutron of mass $m_N$ $(momentum $~ $0)$ a nucleus of mass $M$ breaks into two nuclei of masses $m_1$ and $3m_1$ $(4m_1 = M + m_N)$, respectively. If the de Broglie wavelength of the nucleus with mass $m_1$ is $\lambda$, then de Broglie wavelength of the other nucleus will be
The particle that possesses half integral spin as
The particle that possesses half integral spin as