What do you understand by the dual nature of electron, Derive Broglie equation?
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Louis de Broglie hypothesis:
if radiant energy could, under appropriate circumstances behave as though it were a stream of particles, then could matter, under appropriate circumstances, exhibit wave-like properties?
For example, the electron in orbit around a nucleus. DeBroglie suggested that the electron could be thought of as a wave with a characteristic wavelength.
He proposed that the wavelength of the electron was a function of its mass (m) and its velocity (u):
i.e. the wavelength for "matter waves", where h is Planck's constant and is u velocity (not, the frequency). The quantity mu for any object is its momentum (mass * velocity).
What is the characteristic wavelength of an electron with a velocity of 5.97 x 106 m/s? (the mass of the electron is 9.11 x 10-28 g)
Planck's constant (h) is 6.63 x 10-34 J s (also, recall that 1J = 1 kg m2/s2)
converting g to kg:
Converting from kg m2/s2 to Joules:
The relationship between energy (E) and frequency (n ) for electromagnetic radiation (Planck's quantum of energy)
The relationship between wavelength (l ) and frequency (n ) for electromagnetic radiation
From these relationships, we can determine the relationship between energy and wavelength:
or, rearranging:
The relationship between wavelength (l ) and momentum (m*v) for DeBroglie's "particle wave"
From the above relationships, we can calculate the relationship between energy (E) and momentum (m*v)
Simplify, and solve for E:
The highest velocity (v) attainable by matter is the speed of light (c), therefore, the maximum energy would seem to be:
or
Why do nuclear bombs make such a loud "pop"?
The Fuel value of hydrogen is 142 x 103 J g-1
If all matter were converted into energy
E = 1x10-3kg * (3x108m/s)2
E = 9x1013 kg m2 s-2
E = 9x1013 J
In other words, we can get out about 9 orders of magnitude greater energy if the hydrogen is converted directly into energy, rather than combusting it.
Nuclear fission and fusion reactions convert a fraction of their matter into energy. The bomb that was dropped on Hiroshima contained about 15 kg of the 235Uranium isotope, a fissionable material. The actual amount of mass that was converted into energy is estimated at about 1 kg (releasing around 1 x 1017 J of energy in a split second). The estimated temperature at the moment of detonation is estimated to have been around 5 million degrees. In addition to the sun-like heat, much of the damage was due to the pressure wave that was produced
if radiant energy could, under appropriate circumstances behave as though it were a stream of particles, then could matter, under appropriate circumstances, exhibit wave-like properties?
For example, the electron in orbit around a nucleus. DeBroglie suggested that the electron could be thought of as a wave with a characteristic wavelength.
He proposed that the wavelength of the electron was a function of its mass (m) and its velocity (u):
i.e. the wavelength for "matter waves", where h is Planck's constant and is u velocity (not, the frequency). The quantity mu for any object is its momentum (mass * velocity).
What is the characteristic wavelength of an electron with a velocity of 5.97 x 106 m/s? (the mass of the electron is 9.11 x 10-28 g)
Planck's constant (h) is 6.63 x 10-34 J s (also, recall that 1J = 1 kg m2/s2)
converting g to kg:
Converting from kg m2/s2 to Joules:
The relationship between energy (E) and frequency (n ) for electromagnetic radiation (Planck's quantum of energy)
The relationship between wavelength (l ) and frequency (n ) for electromagnetic radiation
From these relationships, we can determine the relationship between energy and wavelength:
or, rearranging:
The relationship between wavelength (l ) and momentum (m*v) for DeBroglie's "particle wave"
From the above relationships, we can calculate the relationship between energy (E) and momentum (m*v)
Simplify, and solve for E:
The highest velocity (v) attainable by matter is the speed of light (c), therefore, the maximum energy would seem to be:
or
Why do nuclear bombs make such a loud "pop"?
The Fuel value of hydrogen is 142 x 103 J g-1
If all matter were converted into energy
E = 1x10-3kg * (3x108m/s)2
E = 9x1013 kg m2 s-2
E = 9x1013 J
In other words, we can get out about 9 orders of magnitude greater energy if the hydrogen is converted directly into energy, rather than combusting it.
Nuclear fission and fusion reactions convert a fraction of their matter into energy. The bomb that was dropped on Hiroshima contained about 15 kg of the 235Uranium isotope, a fissionable material. The actual amount of mass that was converted into energy is estimated at about 1 kg (releasing around 1 x 1017 J of energy in a split second). The estimated temperature at the moment of detonation is estimated to have been around 5 million degrees. In addition to the sun-like heat, much of the damage was due to the pressure wave that was produced
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