Question

Calculate the wavelength corresponding to a transition of electrons from the n = 6 energy level...

Calculate the wavelength corresponding to a transition of electrons from the n = 6 energy level to the n = 3 level in a B4+ ion. (Use En= -R(z2/n2))

Using your answer from the question above what is the speed that an electron would need to travel in order to display the same wavelength?

Homework Answers

Answer #1

Using the relation:

En= (-2.18 x 10-18 J/mol) Z2/n2

Here Z is the atomic number.

For the boron ion B4+, Z = 5

Putting values in the equation to calculate the energy of transition, we get:

E6 - E3 = (-2.18 x 10-18 ) (52/62 - 52/32) = 82.916 J/mol

Using the Planck's equation:

E = h*(c/), where h is planck's constant = 6.62*10-34 m2.kg/s, c = speed of light = 3*108 m/s,

Putting values and calculating we get:

= 1.4427*10-3 m

For calculating the speed of electron with this much energy, we use the following relation:

E = 0.5*m*v2

Here, m is mass of electron, and v is its velocity

Putting values, we get:

82.916 J = 0.5 * (9.0 * 10-31 kg) * v2

Solve this to calculate v.

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