A nucleus of uranium decays at rest into nuclei of thorium and helium. Then

Question

Differentiate between nuclear fission and fusion.

Answer 1

To understand this question, we need to analyze the decay of a uranium nucleus into thorium and helium nuclei. This process is a typical alpha decay where a uranium nucleus (at rest) emits an alpha particle (helium nucleus) and transforms into a thorium nucleus.

Firstly, let's understand the conservation laws applicable to this nuclear reaction:

Conservation of Momentum: Initially, the uranium nucleus is at rest. Hence, its total momentum is zero. After decay, the thorium and helium nuclei must have equal and opposite momenta to conserve the overall momentum. Thus: p_{\text{thorium}} = -p_{\text{helium}}

Conservation of Energy: The energy released in the decay is distributed as kinetic energy between the thorium nucleus and the helium nucleus.

To elaborate on why the helium nucleus has more kinetic energy than the thorium nucleus, consider the following reasoning:

The momentum (p) of the thorium and helium nuclei are equal in magnitude but opposite in direction as derived from the conservation of momentum: p_{\text{thorium}} = p_{\text{helium}}.
Since momentum p = mv, where m is mass and v is velocity, and given the two momenta are equal: m_{\text{thorium}}v_{\text{thorium}} = m_{\text{helium}}v_{\text{helium}}.
Because the helium nucleus is much lighter than the thorium nucleus (m_{\text{helium}} \ll m_{\text{thorium}}), the helium nucleus must have a much higher velocity than the thorium nucleus to conserve momentum.
The kinetic energy (KE) is given by KE = \frac{1}{2} mv^2. For the same magnitude of momentum, a lighter particle (helium nucleus) with higher velocity will possess greater kinetic energy.
Hence, the helium nucleus has more kinetic energy than the thorium nucleus.

Therefore, the correct answer is: The helium nucleus has more kinetic energy than the thorium nucleus.

Answer 2

To understand this question, we need to analyze the decay of a uranium nucleus into thorium and helium nuclei. This process is a typical alpha decay where a uranium nucleus (at rest) emits an alpha particle (helium nucleus) and transforms into a thorium nucleus.

Firstly, let's understand the conservation laws applicable to this nuclear reaction:

Conservation of Momentum: Initially, the uranium nucleus is at rest. Hence, its total momentum is zero. After decay, the thorium and helium nuclei must have equal and opposite momenta to conserve the overall momentum. Thus: p_{\text{thorium}} = -p_{\text{helium}}

Conservation of Energy: The energy released in the decay is distributed as kinetic energy between the thorium nucleus and the helium nucleus.

To elaborate on why the helium nucleus has more kinetic energy than the thorium nucleus, consider the following reasoning:

The momentum (p) of the thorium and helium nuclei are equal in magnitude but opposite in direction as derived from the conservation of momentum: p_{\text{thorium}} = p_{\text{helium}}.
Since momentum p = mv, where m is mass and v is velocity, and given the two momenta are equal: m_{\text{thorium}}v_{\text{thorium}} = m_{\text{helium}}v_{\text{helium}}.
Because the helium nucleus is much lighter than the thorium nucleus (m_{\text{helium}} \ll m_{\text{thorium}}), the helium nucleus must have a much higher velocity than the thorium nucleus to conserve momentum.
The kinetic energy (KE) is given by KE = \frac{1}{2} mv^2. For the same magnitude of momentum, a lighter particle (helium nucleus) with higher velocity will possess greater kinetic energy.
Hence, the helium nucleus has more kinetic energy than the thorium nucleus.

Therefore, the correct answer is: The helium nucleus has more kinetic energy than the thorium nucleus.

A nucleus of uranium decays at rest into nuclei of thorium and helium. Then

The Correct Option is C

Solution and Explanation

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