Find the de broglie wavelength (in nm) associated with an electron that is moving with a velocity of 5230 km/s. the electron rest mass is 9.11 x 10⁻³¹ kg. note, electrons having this speed would need to be treated as waves in atoms because the wavelength is on the order of the size of atoms.

Explanation:

The de brogllie wavelength is given as

λ = h/mv

where

λ is the de broglie wavelenth

h is the plank constant given as 6.62 × 10-34 m² kg / s

m is the mass of the particle =9.11 x 10⁻³¹ kg

v is the velocity with which the particle moves = 5230 km/s. which as to be converted to m/s by multiplying it by 1000 to give 5230000m/s

hence

λ = 6.62 × 10-34 / 5230000 × 9.11 x 10⁻³¹ =

1.39 ×10^{-10}m

but since the answer must be in nm , we multiply  1.39 ×10^{-10}m  by 10^{9}

then we get 0.139nm

when the volume of gas is   changed from   717.73 ml   to 852 ml   the temperature will   change   from 315   c to 452   c

    calculation

this is calculated using the charles law formula

that is,   v1/t1 = v2/t2

          v1=?

        t1 = 315 c   into   kelvin = 315 +273 = 588 k

        v2 = 852   ml

        t2 = 425c + 273 =698 k

make v1   the subject of the formula ( by   multiplying both side by t1)

  v1=( v2 xt1) / t2

v1= (852 ml   x 588 k)/ 698 k= 717.73 ml