Question

Write an equation for each of the following natural radioactive decay processes: (a) W-160 decays by alpha emission (b) P-32 decays by beta emission (c) Co-55 decays by positron emission (d) Ti- 44 decays by electron capture

Short answer

W-160 emits alpha, P-32 emits beta, Co-55 emits positron, and Ti-44 captures an electron.

Step-by-step solution

Understand Alpha Decay

In alpha decay, an alpha particle, which consists of 2 protons and 2 neutrons, is emitted from the nucleus. This causes the atomic number to decrease by 2 and the mass number to decrease by 4. For W-160 (Tungsten), the atomic number is 74. When it undergoes alpha decay: - Mass number of W decreases from 160 to 156. - Atomic number decreases from 74 to 72. This transforms W (atomic number 74) into Hafnium (Hf) with an atomic number of 72.

Solution to Part (a)

The nuclear equation for the alpha decay of W-160 is:\[_{74}^{160} \text{W} \rightarrow _{72}^{156} \text{Hf} + _{2}^{4} \text{He}\]

Understand Beta Decay

In beta decay, a neutron in the nucleus is transformed into a proton, and a beta particle (an electron) is emitted. This increases the atomic number by 1, while the mass number remains unchanged. For P-32 (Phosphorus), the atomic number is 15. After beta decay: - Atomic number increases from 15 to 16. - Mass number remains 32. This transforms P (atomic number 15) into Sulfur (S) with an atomic number of 16.

Solution to Part (b)

The nuclear equation for the beta decay of P-32 is:\[_{15}^{32} \text{P} \rightarrow _{16}^{32} \text{S} + _{-1}^{0} \text{e}\]

Understand Positron Emission

In positron emission, a proton in the nucleus is converted into a neutron, and a positron (a particle like an electron but with a positive charge) is emitted. This decreases the atomic number by 1, while the mass number remains unchanged. For Co-55 (Cobalt), the atomic number is 27. After positron emission: - Atomic number decreases from 27 to 26. - Mass number remains 55. This transforms Co (atomic number 27) into Iron (Fe) with an atomic number of 26.

Solution to Part (c)

The nuclear equation for the positron emission of Co-55 is:\[_{27}^{55} \text{Co} \rightarrow _{26}^{55} \text{Fe} + _{1}^{0} \text{e}\]

Understand Electron Capture

In electron capture, an electron from the inner shell is captured by the nucleus and combines with a proton to form a neutron, decreasing the atomic number by 1, while the mass number remains unchanged. For Ti-44 (Titanium), the atomic number is 22. After electron capture: - Atomic number decreases from 22 to 21. - Mass number remains 44. This transforms Ti (atomic number 22) into Scandium (Sc) with an atomic number of 21.

Solution to Part (d)

The equation for electron capture of Ti-44 is:\[_{22}^{44} \text{Ti} + _{-1}^{0} \text{e} \rightarrow _{21}^{44} \text{Sc}\]

Key concepts

Alpha Decay

Alpha decay is a type of radioactive decay where an unstable nucleus releases an alpha particle to become more stable. An alpha particle is essentially a helium nucleus, consisting of 2 protons and 2 neutrons. When this particle is emitted, it causes a decrease in the mass number by 4 and the atomic number by 2 in the parent nucleus.

For example, in the alpha decay of W-160 (Tungsten), the initial mass number of 160 reduces to 156, and the atomic number decreases from 74 to 72, forming Hafnium (Hf). The transformation can be represented by the nuclear equation: \[_{74}^{160} \text{W} \rightarrow _{72}^{156} \text{Hf} + _{2}^{4} \text{He}\]

This process illustrates the classical conversion of one element to another via alpha emission.

Beta Decay

Beta decay involves a neutron in the nucleus transforming into a proton and emitting a beta particle, which is an electron. This conversion results in an increase in the atomic number by 1, while the mass number remains unchanged.

For example, when Phosphorus-32 undergoes beta decay, the atomic number increases from 15 to 16, transforming into Sulfur-32. The mass number of the compound stays at 32. This transformation is expressed in the equation:\[_{15}^{32} \text{P} \rightarrow _{16}^{32} \text{S} + _{-1}^{0} \text{e}\]

Beta decay is a process that occurs when a neutron-to-proton transformation aids in stabilizing a nucleus that previously had a neutron excess.

Positron Emission

Positron emission is a type of beta decay process where a proton is converted into a neutron while emitting a positron. A positron is the antiparticle of an electron, meaning it carries a positive charge.

This transition causes the atomic number to decrease by 1 without altering the mass number. For instance, Cobalt-55's positron emission leads to a decrease in its atomic number from 27 to 26, forming Iron (Fe), while its mass number remains at 55. The nuclear equation for this process is:\[_{27}^{55} \text{Co} \rightarrow _{26}^{55} \text{Fe} + _{1}^{0} \text{e}\]

Positron emission helps stabilize a nucleus with an excess of protons, encouraging the shift towards a more balanced nuclear state.

Electron Capture

In electron capture, an electron from the inner atomic shell is drawn into the nucleus, where it combines with a proton to form a neutron. This results in a decrease in the atomic number by 1, as one proton is effectively turned into a neutron, without affecting the mass number.

For example, Titanium-44 experiences electron capture and transforms from an element with an atomic number of 22 to Scandium (Sc) with an atomic number of 21. The mass number stays constant at 44. The nuclear equation representing this process is:\[_{22}^{44} \text{Ti} + _{-1}^{0} \text{e} \rightarrow _{21}^{44} \text{Sc}\]

Electron capture is typically observed in proton-rich nuclei, aiding in stabilizing them by effectively reducing the proton-to-neutron ratio.