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In order for a thermonuclear fusion reaction of two deuterons (2^1H^+) to take place, the deuterons must collide and each must have a velocity of about 1 * 10^6 m/s. Find the wavelength of such a deuteron.
Ch.7 - Quantum-Mechanical Model of the Atom
Chapter 7, Problem 89
The iodine molecule can be photodissociated (broken apart with light) into iodine atoms in the gas phase with light of wavelengths shorter than about 792 nm. A 100.0-mL glass tube contains 55.7 mtorr of gaseous iodine at 25.0 °C. What is the minimum amount of light energy that must be absorbed by the iodine in the tube to dissociate 15.0% of the molecules?
Verified step by step guidance1
Convert the pressure from mtorr to atm by using the conversion factor: 1 atm = 760 torr.
Use the ideal gas law, PV = nRT, to calculate the number of moles of iodine gas (I2) in the tube. Remember to convert the volume to liters and use the appropriate value for R (0.0821 L·atm/mol·K).
Calculate the number of moles of iodine molecules that need to be dissociated by multiplying the total moles by 15.0%.
Determine the energy required to dissociate one mole of iodine molecules using the wavelength of light (792 nm) and the equation E = hc/λ, where h is Planck's constant and c is the speed of light.
Calculate the total energy required to dissociate the calculated moles of iodine molecules by multiplying the energy per mole by the number of moles to be dissociated.
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