Question

The increasing order (lowest first) for the values of \(\mathrm{e} / \mathrm{m}\) (charge/mass) for electron (e), proton (p), neutron (n) and alpha particle (a) is: (a) \(\mathrm{n}, \mathrm{p}, \mathrm{a}, \mathrm{e}\) (b) \(\mathrm{n}, \mathrm{p}, \mathrm{e}, \mathrm{a}\) (c) \(\mathrm{n}, \mathrm{a}, \mathrm{p}, \mathrm{e}\) (d) e, p, n, a

Short answer

(c) \( \mathrm{n}, \mathrm{a}, \mathrm{p}, \mathrm{e} \) is the correct order.

Step-by-step solution

Understand the Problem

We need to order the particles (electron, proton, neutron, alpha particle) by their charge-to-mass ratio \( \left( \frac{e}{m} \right) \). Generally, the concept is that the higher the charge-to-mass ratio, the quicker the particle is influenced by an electric field. Note that neutrons have no charge, so their ratio \( \frac{e}{m} \) is zero.

Charge and Mass of Each Particle

1. **Electron (e):** Charge = \(-e\), Mass \( m_e \)2. **Proton (p):** Charge = \(+e\), Mass \( m_p \)3. **Neutron (n):** Charge = 0, Mass \( m_n \)4. **Alpha particle (a):** Charge = \(+2e\), Mass \( 4m_p \) (since it consists of 2 protons and 2 neutrons)

Calculate \( \frac{e}{m} \) for each particle

1. **Neutron (n):** \( \frac{e}{m} = \frac{0}{m_n} = 0 \)2. **Proton (p):** \( \frac{e}{m} = \frac{e}{m_p} \)3. **Alpha particle (a):** \( \frac{e}{m} = \frac{2e}{4m_p} = \frac{e}{2m_p} \)4. **Electron (e):** \( \frac{e}{m} = \frac{-e}{m_e} \approx \frac{1.6 \times 10^{-19} C}{9.11 \times 10^{-31} kg} \approx 1.76 \times 10^{11} C/kg \) (in magnitude)

Compare and Order

- **Neutron (n):** \( \frac{e}{m} = 0 \)- **Alpha particle (a):** \( \frac{e}{m} = \frac{e}{2m_p} \) is less than \( \frac{e}{m} \) of a proton.- **Proton (p):** \( \frac{e}{m} = \frac{e}{m_p} \)- **Electron (e):** \( \frac{e}{m} \) (magnitude) is significantly larger than \( \frac{e}{m} \) of a proton due to its much smaller mass.

Arrange In Increasing Order

Arrange the particles in increasing order based on their \( \frac{e}{m} \) values: neutron (n) < alpha particle (a) < proton (p) < electron (e).

Key concepts

Electron

Electrons are subatomic particles with a negative charge. They are incredibly small compared to other particles such as protons and neutrons. Due to their significantly smaller mass, electrons have the highest charge-to-mass ratio among the particles discussed here.

The charge of an electron is \(-e\), which is approximately \(1.6 \times 10^{-19}\) coulombs. The mass of an electron is around \(9.11 \times 10^{-31}\) kilograms. Because of this small mass, the charge-to-mass ratio \( \left( \frac{e}{m} \right) \) for an electron comes out to be very high, about \(1.76 \times 10^{11}\) C/kg in magnitude.

This high ratio means electrons respond very quickly and strongly to electric fields. This property is crucial in many applications, from household appliances to complex electronic circuits.

Proton

Protons are positively charged particles found in the nucleus of an atom. Along with neutrons, they provide most of the atom's mass. The charge of a proton is equal in magnitude but opposite in sign to that of an electron, resulting in \(+e\), or about \(1.6 \times 10^{-19}\) coulombs.

The mass of a proton is considerably larger than that of an electron and is estimated to be \(1.67 \times 10^{-27}\) kilograms. This results in a charge-to-mass ratio \( \left( \frac{e}{m} \right) \) that is lower than that of an electron. However, even though it's lower, the proton's charge-to-mass ratio is still larger than that of an alpha particle, due to the latter's higher mass.

The presence and behavior of protons are essential for defining the chemical identity of an atom, as the number of protons determines the element and its properties.

Neutron

Neutrons are neutral particles, meaning they have no electric charge. They are found in the atomic nucleus alongside protons. Despite having no charge, neutrons have a mass nearly identical to that of protons, approximately \(1.67 \times 10^{-27}\) kilograms.

Since the charge of a neutron is zero, the charge-to-mass ratio \( \left( \frac{e}{m} \right) \) for neutrons is also zero. Therefore, neutrons do not respond to electric fields like charged particles do, but they play a vital role in the stability of the nucleus.

Neutrons are key to the process of nuclear reactions and play a critical role in nuclear fission and fusion. They also explain why isotopes of the same element can exist, differing only by the number of neutrons present.

Alpha Particle

Alpha particles consist of two protons and two neutrons bound together, making them quite massive compared to individual electrons and protons. Because they include two protons, they possess a charge of \(+2e\), equating to about \(3.2 \times 10^{-19}\) coulombs.

The mass of an alpha particle is approximately four times that of a single proton, roughly \(6.64 \times 10^{-27}\) kilograms. This substantial mass results in an alpha particle's charge-to-mass ratio \( \left( \frac{e}{m} \right) \), \( \frac{e}{2m_p} \), being much smaller than that of a proton and significantly less than that of an electron.

Alpha particles are typically emitted during alpha decay, a nuclear process by which heavy elements lose part of their mass. While alpha particles are not greatly penetrative, they can cause substantial damage to biological tissues if ingested or inhaled.