To determine the increasing order of $$\frac{e}{m}$$ (charge-to-mass ratio) for electron (e), proton (p), neutron (n), and alpha particle ($$\alpha$$), we need to understand the properties of these particles:

Electron (e): The electron has a charge of $$-1.6 \times 10^{-19} \text{C} $$ and a mass of approximately $$9.11 \times 10^{-31} \text{kg}.$$

Proton (p): The proton has a charge of $$+1.6 \times 10^{-19} \text{C} $$ and a mass of approximately $$1.67 \times 10^{-27} \text{kg}.$$

Neutron (n): The neutron has no charge ($$0 \text{C}$$) and a mass of approximately $$1.67 \times 10^{-27} \text{kg}.$$ Since the charge is zero, the charge-to-mass ratio for a neutron is effectively $$0.$$

Alpha Particle ($$\alpha$$): An alpha particle consists of 2 protons and 2 neutrons, with a total charge of $$2 \times 1.6 \times 10^{-19} \text{C}$$ and a total mass of approximately $$4 \times 1.67 \times 10^{-27} \text{kg} = 6.68 \times 10^{-27} \text{kg}.$$

Now, let's calculate the $$\frac{e}{m}$$ values for each of these particles (except for neutron where this value is 0 because it has no charge):

For an electron, $$\frac{e}{m} = \frac{1.6 \times 10^{-19}}{9.11 \times 10^{-31}} \approx 1.76 \times 10^{11} \frac{C}{kg}$$

For a proton, $$\frac{e}{m} = \frac{1.6 \times 10^{-19}}{1.67 \times 10^{-27}} \approx 9.58 \times 10^{7} \frac{C}{kg}$$

For an alpha particle, $$\frac{e}{m} = \frac{2 \times 1.6 \times 10^{-19}}{6.68 \times 10^{-27}} \approx 4.79 \times 10^{7} \frac{C}{kg}$$

Therefore, in increasing order of the charge-to-mass ratio ($$\frac{e}{m}$$), we have:

Neutron (n) with $$0 \frac{C}{kg}$$

Alpha particle ($$\alpha$$) with $$4.79 \times 10^{7} \frac{C}{kg}$$

Proton (p) with $$9.58 \times 10^{7} \frac{C}{kg}$$

Electron (e) with $$1.76 \times 10^{11} \frac{C}{kg}$$

The correct order is then n, $$\alpha$$, p, e, which corresponds to:

Option D: n, $$\alpha$$, p, e