[College Chem] kinetic energy problem

[Lori]

Homework Statement

[/B]
atom traveling at 1.00% the speed of light has a KE of 2.016x10-16 kJ. Identify the element.

Homework Equations

[/B]
KE = .5mv^2
Hv= binding energy + KE

The Attempt at a Solution

[/B]
Ok. So I plugged into velocity and me to find my mass and got like 4.48E-26 g. So I tried to convert to grams/mol but it doesn't match with any of the elements on the periodic table... What do I do?

 

[Lori]

I also have the solution but still want to know how to get the answer.

Answer : 27g/mol Aluminum

 

[I like Serena]

Homework Statement

atom traveling at 1.00% the speed of light has a KE of 2.016x10-16 kJ. Identify the element. [/B]

Homework Equations

KE = .5mv^2
Hv= binding energy + KE[/B]

The Attempt at a Solution

Ok. So I plugged into velocity and me to find my mass and got like 4.48E-26 g. So I tried to convert to grams/mol but it doesn't match with any of the elements on the periodic table... What do I do?[/B]

I also have the solution but still want to know how to get the answer.

Answer : 27g/mol Aluminum

Hi Lori! Welcome to PF! :)

The mass should be 4.48E-26 kg (kilograms), which we should divide by the average mass of a proton and a neutron, the so called unified atomic mass unit (u), which is 1.66E-27 kg/u.
The result is 27.0 u, which corresponds to the atomic mass of Aluminium, and which is also its number of grams per mol.

 

[Lori]

Shouldn't the mass be 4.48E-29 kg?

[2(2.016E-16)] / [0.01* (3.00E8)] = 4.48E-29kg

the units for KE is kgm^2/s^2 if I'm correct and so the kg is left and i get 4.48E-29kg

 

[I like Serena]

Note that the energy is given in kilo joules. There is a hidden factor 1000 in there. And that's while the kilogram (including the kilo) is part of the joule.
In other words, we have: 1 kJ = 1000 kg.m²/s².

 

[Lori]

Thank you. I did not know that!