Question

An alpha particle (mass 6.6 x 10^-24 grams) emitted by radium travels at 3.4 x 10^7 plus or minus 0.1 x 10^7 mi/h.

(a) What is its de Broglie wavelength (in meters)?

(b) Whats uncertainty in its position?

for part (a) I got 1.53 meters which said it was wrong on Aris and I got 1.56 x 10^-56 meters for part (b) the uncertainty which said it was wrong too.

This is how I solved it please tell me what I did wrong:

part (a) lambda =h/mu

first convert mi/hr to meters/sec
3.4 x 10^7mi/hr = 1.52 x 10^7m/s

(6.626 x 10^-34 kg m^2 s)/(6.6 X 10^-27 kg)x(1.52 x 10^7 m/s)
= 1.53 meters

part (b) delta(x) x m delta u is greater than or equal to h/4 pi.

so, delta (x) is greater than or equal to (h)/ (4 pi) x (m) delta (u)

delta x= (6.626 x 10^-34 kg m^2 s)/ (4 pi) x (6.6 x 10^-27 kg)(4.48 x 10^5 m/s)
= 1.56 x 10^-55 meters

I also converted the mass 6.6 x 10^-24 grams into kilograms, making it 6.6 x 10^-27 kilograms.

Please look this over and correct my error, thank you.

Answer 1

please help me, Aris closes in 35 minutes. it's urgent!

Answer 2

I think you have converted from miles/hour to m/s correctly. But when I put that into the equation, which you appear to have set up correctly, I don't get your answer but something like 6 x 10^-15 or so meters.

Answer 3

Run that calculation through your calculator again and see what you get.