Which of the following figures represents the variation of particle momentum $p$ and the associated de-Broglie wavelength $\lambda$?

The de Broglie wavelength of an electron moving with a velocity $1.5 \times 10^8 \, m/s$ is equal to that of a photon. The ratio of the kinetic energy of the electron to the energy of the photon is

If the kinetic energy of a particle is increased by $16$ times, the percentage change in the de Broglie wavelength of the particle is......... $\%$

The temperature of an ideal gas in $3$-dimensions is $300\, K$. The corresponding de-Broglie wavelength of the electron approximately at $300\, K$ is $....\, nm$.
$[m_e = \text{mass of electron} = 9 \times 10^{-31}\, kg, h = \text{Planck constant} = 6.6 \times 10^{-34}\, Js, k_B = \text{Boltzmann constant} = 1.38 \times 10^{-23}\, JK^{-1}]$

If the momentum of an electron is changed by $\Delta p,$ then the de-Broglie wavelength associated with it changes by $0.50\%.$ The initial momentum of the electron will be:

The speed of an electron having a wavelength of $10^{-10} \ m$ is ................. $ \times 10^6 \ m/s$.