Scientists are working hard to develop nuclear fusion reactor. Nuclei of heavy hydrogen, `._(1)^(2)H`, Known as deutreron and denoted by `D`, can be throught of as a candidate for fusion reactor. The `D-D` reaction is `._(1)^(2)H+._(1)^(2)Hrarr._(2)^(2)He+n+"energy"`. In the core of fusion reactor, a gas of heavy hydrogen is fully ionized into deuteron nuclei and electrons. This collection of `._(1)^(2)H` nuclei and electrons is known as plasma. The nuclei move randomly in the reactor core and occasionally come close enough for nuclear fusion to take place. Usually, the temperatures in the reactor core are too high and no material wall can be used to confine the plasma. Special techniques are used which confine the plasma for a time `t_(0)` before the particles fly away from this core. If `n` is the density (number`//` volume) of deuterons, hte product `nt_(0)` is called Lawson number. In one of the criteria, a reactor is termed successful if Lawson is greater than `5xx10^(14)s//cm^(3)`.
It may be helpful to use the following. Boltzman constant `K=8.6xx10^(-5)eV//K, (e^(2))/(4piepsilon_(0))=1.44xx10^(-9)eVm`.
Assume that two deuteron nuclei in the core of fusion reactor at temperature `T` are moving towards each other, each with kinetic energy `1. 5 kT`, when the separation between them is large enough to neglect. Coulomb potential energy. Also neglect any interaction from other particles in the core. The minimum temperature `T` required for them to reach a separation of `4xx10^(-15)m` in the range.
Scientists are working hard to develop nuclear fusion reactor. Nuclei of heavy hydrogen, `._(1)^(2)H`, Known as deutreron and denoted by `D`, can be throught of as a candidate for fusion reactor. The `D-D` reaction is `._(1)^(2)H+._(1)^(2)Hrarr._(2)^(2)He+n+"energy"`. In the core of fusion reactor, a gas of heavy hydrogen is fully ionized into deuteron nuclei and electrons. This collection of `._(1)^(2)H` nuclei and electrons is known as plasma. The nuclei move randomly in the reactor core and occasionally come close enough for nuclear fusion to take place. Usually, the temperatures in the reactor core are too high and no material wall can be used to confine the plasma. Special techniques are used which confine the plasma for a time `t_(0)` before the particles fly away from this core. If `n` is the density (number`//` volume) of deuterons, hte product `nt_(0)` is called Lawson number. In one of the criteria, a reactor is termed successful if Lawson is greater than `5xx10^(14)s//cm^(3)`.
It may be helpful to use the following. Boltzman constant `K=8.6xx10^(-5)eV//K, (e^(2))/(4piepsilon_(0))=1.44xx10^(-9)eVm`.
Assume that two deuteron nuclei in the core of fusion reactor at temperature `T` are moving towards each other, each with kinetic energy `1. 5 kT`, when the separation between them is large enough to neglect. Coulomb potential energy. Also neglect any interaction from other particles in the core. The minimum temperature `T` required for them to reach a separation of `4xx10^(-15)m` in the range.
It may be helpful to use the following. Boltzman constant `K=8.6xx10^(-5)eV//K, (e^(2))/(4piepsilon_(0))=1.44xx10^(-9)eVm`.
Assume that two deuteron nuclei in the core of fusion reactor at temperature `T` are moving towards each other, each with kinetic energy `1. 5 kT`, when the separation between them is large enough to neglect. Coulomb potential energy. Also neglect any interaction from other particles in the core. The minimum temperature `T` required for them to reach a separation of `4xx10^(-15)m` in the range.
A
`1.0 xx 10^(9) K lt T lt 2.0 xx 10^(9) K`
B
`2.0 xx 10^(9) K lt T lt 3.0 xx 10^(9) K`
C
`3.0 xx 10^(9) K lt T lt 4.0 xx 10^(9) K`
D
`4.0 xx 10^(9) K lt T lt 5.0 xx 10^(9) K`
Text Solution
Verified by Experts
The correct Answer is:
A
`(3/2 KT)2=(Kq_(1)q_(2))/(r) 3KT=(Kq_(1)q_(2))/(r)`
`T=(1.44xx10^(-9))/(4xx10^(-15)xx3xx8.5xx10^(-5))`
`T=1.39xx10^(9)K" "1xx10^(9) lt T lt 2xx10^(9)K`
`T=(1.44xx10^(-9))/(4xx10^(-15)xx3xx8.5xx10^(-5))`
`T=1.39xx10^(9)K" "1xx10^(9) lt T lt 2xx10^(9)K`
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Assume that two deuteron nuclei in the core of fusion reactor at temperature energy T are moving toward each other, each with kinetic energy 1.5 kT , when the separation between them is large enough to neglect coulomb potential energy . Also neglect any interaction from other particle in the core . The minimum temperature T required for them to reach a separation of 4 xx 10^(-15) m is in the range
Scientists are working hard to develop nuclear fusion reactor Nuclei of heavy hydrogen, _(1)^(2)H , known as deuteron and denoted by D , can be thought of as a candidate for fusion rector . The D-D reaction is _(1)^(2) H + _(1)^(2) H rarr _(2)^(1) He + n+ energy. In the core of fusion reactor, a gas of heavy hydrogen of _(1)^(2) H is fully ionized into deuteron nuclei and electrons. This collection of _1^2H nuclei and electrons is known as plasma . The nuclei move randomly in the reactor core and occasionally come close enough for nuclear fusion to take place. Usually , the temperature in the reactor core are too high and no material will can be used to confine the to plasma for a time t_(0) before the particles fly away from the core. If n is the density (number volume ) of deuterons , the product nt_(0) is called Lawson number. In one of the criteria , a reactor is termed successful if Lawson number is greater then 5 xx 10^(14) s//cm^(2) it may be helpfull to use the following boltzmann constant k = 8.6 xx 10^(-5)eV//k, (e^(2))/(4 pi s_(0)) = 1.44 xx 10^(-9) eVm Assume that two deuteron nuclei in the core of fusion reactor at temperature energy T are moving toward each other, each with kinectic energy 1.5 kT , when the seperation between them is large enough to neglect coulomb potential energy . Also neglate any interaction from other particle in the core . The minimum temperature T required for them to reach a separation of 4 xx 10^(-15) m is in the range
Scientists are working hard to develop nuclear fusion reactor Nuclei of heavy hydrogen, _(1)^(2)H , known as deuteron and denoted by D , can be thought of as a candidate for fusion rector . The D-D reaction is _(1)^(2) H + _(1)^(2) H rarr _(2)^(1) He + n+ energy. In the core of fusion reactor, a gas of heavy hydrogen of _(1)^(2) H is fully ionized into deuteron nuclei and electrons. This collection of _1^2H nuclei and electrons is known as plasma . The nuclei move randomly in the reactor core and occasionally come close enough for nuclear fusion to take place. Usually , the temperature in the reactor core are too high and no material will can be used to confine the to plasma for a time t_(0) before the particles fly away from the core. If n is the density (number volume ) of deuterons , the product nt_(0) is called Lawson number. In one of the criteria , a reactor is termed successful if Lawson number is greater then 5 xx 10^(14) s//cm^(2) it may be helpfull to use the following boltzmann constant lambda = 8.6 xx 10^(-5)eV//k, (e^(2))/(4 pi s_(0)) = 1.44 xx 10^(-9) eVm Assume that two deuteron nuclei in the core of fusion reactor at temperature energy T are moving toward each other, each with kinectic energy 1.5 kT , when the seperation between them is large enough to neglect coulomb potential energy . Also neglate any interaction from other particle in the core . The minimum temperature T required for them to reach a separation of 4 xx 10^(-15) m is in the range
Scientists are working hard to develop nuclear fusion reactor Nuclei of heavy hydrogen, _(1)^(2)H , known as deuteron and denoted by D , can be thought of as a candidate for fusion rector . The D-D reaction is _(1)^(2) H + _(1)^(2) H rarr _(2)^(1) He + n+ energy. In the core of fusion reactor, a gas of heavy hydrogen of _(1)^(2) H is fully ionized into deuteron nuclei and electrons. This collection of _1^2H nuclei and electrons is known as plasma . The nuclei move randomly in the reactor core and occasionally come close enough for nuclear fusion to take place. Usually , the temperature in the reactor core are too high and no material will can be used to confine the to plasma for a time t_(0) before the particles fly away from the core. If n is the density (number volume ) of deuterons , the product nt_(0) is called Lawson number. In one of the criteria , a reactor is termed successful if Lawson number is greater then 5 xx 10^(14) s//cm^(2) it may be helpfull to use the following boltzmann constant lambda = 8.6 xx 10^(-5)eV//k, (e^(2))/(4 pi s_(0)) = 1.44 xx 10^(-9) eVm In the core of nucleus fusion reactor , the gas become plasma because of
Scientists are working hard to develop nuclear fusion reactor Nuclei of heavy hydrogen, _(1)^(2)H , known as deuteron and denoted by D , can be thought of as a candidate for fusion rector . The D-D reaction is _(1)^(2) H + _(1)^(2) H rarr _(2)^(1) He + n+ energy. In the core of fusion reactor, a gas of heavy hydrogen of _(1)^(2) H is fully ionized into deuteron nuclei and electrons. This collection of _1^2H nuclei and electrons is known as plasma . The nuclei move randomly in the reactor core and occasionally come close enough for nuclear fusion to take place. Usually , the temperature in the reactor core are too high and no material will can be used to confine the to plasma for a time t_(0) before the particles fly away from the core. If n is the density (number volume ) of deuterons , the product nt_(0) is called Lawson number. In one of the criteria , a reactor is termed successful if Lawson number is greater then 5 xx 10^(14) s//cm^(2) it may be helpfull to use the following boltzmann constant lambda = 8.6 xx 10^(-5)eV//k, (e^(2))/(4 pi s_(0)) = 1.44 xx 10^(-9) eVm In the core of nucleus fusion reactor , the gas become plasma because of
Scientists are working hard to develop nuclear fusion reactor Nuclei of heavy hydrogen, _(1)^(2)H , known as deuteron and denoted by D , can be thought of as a candidate for fusion rector . The D-D reaction is _(1)^(2) H + _(1)^(2) H rarr _(2)^(1) He + n+ energy. In the core of fusion reactor, a gas of heavy hydrogen of _(1)^(2) H is fully ionized into deuteron nuclei and electrons. This collection of _1^2H nuclei and electrons is known as plasma . The nuclei move randomly in the reactor core and occasionally come close enough for nuclear fusion to take place. Usually , the temperature in the reactor core are too high and no material will can be used to confine the to plasma for a time t_(0) before the particles fly away from the core. If n is the density (number volume ) of deuterons , the product nt_(0) is called Lawson number. In one of the criteria , a reactor is termed successful if Lawson number is greater then 5 xx 10^(14) s//cm^(2) it may be helpfull to use the following boltzmann constant lambda = 8.6 xx 10^(-5)eV//k, (e^(2))/(4 pi s_(0)) = 1.44 xx 10^(-9) eVm Result of calculations for four different design of a fusion reactor using D-D reaction are given below. which of these is most promising based on Lawson criterion ?
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