The wavelength of an electron and a neutron will become equal when the velocity of the electron is $$x$$ times the velocity of neutron. The value of $$x$$ is ______ (the nearest integer) (Mass of electron is $$9.1 \times 10^{-31} \text{ kg}$$ and mass of neutron is $$1.6 \times 10^{-27} \text{ kg}$$)

We need to find the value of $$x$$ such that the velocity of the electron is $$x$$ times the velocity of the neutron when their de Broglie wavelengths are equal.

The de Broglie wavelength is given by:

$$\lambda = \frac{h}{mv}$$

where $$h$$ is Planck's constant, $$m$$ is the mass, and $$v$$ is the velocity of the particle.

For the electron and neutron to have the same wavelength:

$$\lambda_e = \lambda_n$$

$$\frac{h}{m_e v_e} = \frac{h}{m_n v_n}$$

Cancelling $$h$$ from both sides:

$$\frac{1}{m_e v_e} = \frac{1}{m_n v_n}$$

$$m_n v_n = m_e v_e$$

$$\frac{v_e}{v_n} = \frac{m_n}{m_e}$$

$$m_e = 9.1 \times 10^{-31} \text{ kg}$$

$$m_n = 1.6 \times 10^{-27} \text{ kg}$$

$$x = \frac{v_e}{v_n} = \frac{m_n}{m_e} = \frac{1.6 \times 10^{-27}}{9.1 \times 10^{-31}}$$

$$x = \frac{1.6}{9.1} \times 10^{-27-(-31)} = \frac{1.6}{9.1} \times 10^{4}$$

$$= 0.17582 \times 10^{4}$$

$$= 1758.2$$

Rounding to the nearest integer: $$x = 1758$$

Hence, the value of $$x$$ is 1758.