Show that the energy of a simple harmonic oscillator in the n = 1 state is 3ℏω/2 by substituting the wave function ψ1 = axe-αx2/2 directly into the schroedinger equation, as broken down in the following steps. first, calculate dψ1/dx, using a, x, and α. dψ1/dx = second, calculate d2ψ1/dx2, using a, x, and α. d2ψ1/dx2 = third, calculate α2x2ψ1 - d2ψ1/dx2, using a, x, and α. α2x2ψ1 - d2ψ1/dx2 = fourth, calculate (α2x2ψ1 - d2ψ1/dx2)/ψ1, using a, x, and α. (α2x2ψ1 - d2ψ1/dx2)/ψ1 = finally, calculate e ≡ [(α2x2ψ1 - d2ψ1/dx2)/ψ1]ℏ2/(2m), using a, x, α, m, ω, and ℏ. e ≡

the only real purpose of sputnik 1 was to beat the us into space. we were getting close to launching a useful satellite, explorer 1 - which launched on january 31, 1958. the ussr had to beat that, so they launched sputnik 1 on october 4, 19

it is given that trillions of microbes make up to 1% to 3% of the body mass.

let's take average of this percentage: 2%

consider the average mass of the human body as 70 kg.

then, trillions of microbes would have mass  

therefore, 100 trillion micro-organisms would weigh:

this is an approximate value and could change depending on the mass of the human body and percentage of the microbes present in it.

average mass per microorganism =