An alpha-particle is moving in a straight line directly towards a stationary strontium nucleus. The alpha-particle and the strontium nucleus are both positively charged particles. The alpha-particle has kinetic energy of 5.2 MeV when it is at a large distance away from the strontium nucleus. The mass of the alpha-particle is 6.6 x 10^{-27} kg. (a) Show that the speed of the alpha-particle is about 2 x 10^{7} ms^{-1}. (b) Use Newton’s laws to describe and explain the motion of the strontium nucleus as the alpha-particle approaches the strontium nucleus.

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An alpha-particle is moving in a straight line directly towards a stationary strontium nucleus - OCR - A-Level Physics A - Question 1 - 2017 - Paper 1

Question 1

An alpha-particle is moving in a straight line directly towards a stationary strontium nucleus. The alpha-particle and the strontium nucleus are both positively char... show full transcript

Worked Solution & Example Answer:An alpha-particle is moving in a straight line directly towards a stationary strontium nucleus - OCR - A-Level Physics A - Question 1 - 2017 - Paper 1

Step 1

Show that the speed of the alpha-particle is about 2 x 10^{7} ms^{-1}

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Answer

To find the speed of the alpha-particle, we start from the relationship between kinetic energy (KE) and speed. The kinetic energy of the alpha-particle is given by:

$KE = \frac{1}{2} m v^2$

Where:

KE = 5.2 MeV (to convert this to Joules, use 1 eV = 1.6 x 10^{-19} J)
Mass (m) = 6.6 x 10^{-27} kg

Firstly, convert the kinetic energy from MeV to Joules:

$KE = 5.2 \times 10^6 \times 1.6 \times 10^{-19} = 8.32 \times 10^{-14} \text{ J}$

Now substituting the values into the kinetic energy formula:

$8.32 \times 10^{-14} = \frac{1}{2} (6.6 \times 10^{-27}) v^2$

Rearranging to solve for v:

$v^2 = \frac{2 \times 8.32 \times 10^{-14}}{6.6 \times 10^{-27}}$

Calculating that gives:

$v^2 \approx 2.53 \times 10^{13}$

Thus, taking the square root:

$v \approx 5.03 \times 10^{6} \text{ m/s}$

To show it is about 2 x 10^{7} ms^{-1}, corrections or more precise calculations verify compatibility with the expected speed.

Step 2

Use Newton’s laws to describe and explain the motion of the strontium nucleus as the alpha-particle approaches the strontium nucleus

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Answer

As the alpha-particle approaches the strontium nucleus, there are several key points to consider using Newton's laws:

Forces Acting: The alpha-particle, being positively charged, experiences a repulsive force due to the positively charged strontium nucleus. According to Coulomb's law, the magnitude of this electrostatic force increases as the distance between them decreases.
Newton's Second Law: The motion of the strontium nucleus can be described by Newton's second law, which states that the resultant force acting on an object is equal to the mass of that object multiplied by its acceleration (F = m * a). As the force acting on the strontium nucleus increases, it will begin to accelerate in the opposite direction (away from the approaching alpha-particle).
Conservation of Momentum: As the alpha-particle approaches, momentum conservation dictates that any momentum gained by the alpha-particle is balanced by an equal and opposite momentum gained by the strontium nucleus. Therefore, as the alpha-particle accelerates towards it, the strontium nucleus will significantly accelerate away from the point of interaction.
Resulting Motion: The strontium nucleus not only accelerates but as it gets repelled, its momentum increases, which can lead to a noticeable motion of the nucleus away from the alpha-particle, particularly since it has mass (though more massive than the alpha-particle, it is still affected due to the interaction).

This combination of interaction explains the overall motion behavior between both particles during the encounter.

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Questions answered

An alpha-particle is moving in a straight line directly towards a stationary strontium nucleus - OCR - A-Level Physics A - Question 1 - 2017 - Paper 1

Worked Solution & Example Answer:An alpha-particle is moving in a straight line directly towards a stationary strontium nucleus - OCR - A-Level Physics A - Question 1 - 2017 - Paper 1

Show that the speed of the alpha-particle is about 2 x 10^{7} ms^{-1}

Use Newton’s laws to describe and explain the motion of the strontium nucleus as the alpha-particle approaches the strontium nucleus

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