In an atom, an electron is moving with a speed of 600 m/s with an accuracy of 0.005%. Certainity with which the position of the electron can be located is (h = 6.6 $$\times$$ 10^-34 kg m²s^-1, mass of electron, e_m = 9.1 $$\times$$ 10^-31 kg)

Calculate the wavelength (in nanometer) associated with a proton moving at 1.0 x 10³ ms⁻¹ (Mass of proton = 1.67 $$\times$$ 10^-27 kg and h = 6.63 $$\times$$ 10^-34 Js) :

Statement - 1 : The variance of first n even natural numbers is $${{{n^2} - 1} \over 4}$$

Statement - 2 : The sum of first n natural numbers is $${{n\left( {n + 1} \right)} \over 2}$$ and the sum of squares of first n natural numbers is $${{n\left( {n + 1} \right)\left( {2n + 1} \right)} \over 6}$$

If the mean deviation of number 1, 1 + d, 1 + 2d,........, 1 + 100d from their mean is 255, then the d is equal to