The confirmation hearing for Chuck Hagel as defense secretary on Thursday will provide senators with a critical opportunity to probe the nominee's views on Iran's nuclear-weapons program. Let's hope the hearing is more illuminating than last week's listless hearing for John Kerry as secretary of state. Some enlightenment about the administration's attitude toward Iran in President Obama's second term would be helpful.

Meanwhile, on Jan. 18, Herman Nackaerts, the chief inspector of the International Atomic Energy Agency, returned to Vienna from Iran after once again being barred from inspecting the Parchin military facility, where weaponization work has likely been underway. The charade of talks about the inspection will resume on Feb. 12. The Iranian regime is also toying with the West on restarting more general negotiations about its nuclear program.

Yet Mr. Obama, still misreading the ayatollahs, appears to remain fixed on the notion Iran can be cajoled or pressured into ending its 20-year drive for nuclear weapons. While earlier diplomacy rested on political mistakes in reading Iran's intentions, recent efforts have added debilitating mistakes in basic physics.

For the past decade, too many in the West hoped that negotiations, accompanied by incentives and disincentives, would lead Iran to renounce nuclear weapons. Until recently, the sine qua non of every diplomatic initiative has been that Tehran must cease all enrichment-related activities. Iran, however, has consistently rejected any limits on enrichment, supposedly for reactor fuel or medical research, and protracted negotiations have gained the regime valuable time to perfect and expand its nuclear program.

The West has fundamentally weakened its case by accepting Iran's line that the Nuclear Non-Proliferation Treaty provides the country with a "right" to "peaceful" nuclear activities. This claim distorts basic treaty principles. Tehran cannot claim treaty "rights" while simultaneously violating parallel commitments not to pursue nuclear weapons. Materially breaching a treaty voids the entire agreement, including "rights" found elsewhere in the deal. Iran has readily exploited the West's bad lawyering and worse political judgment, and it has made no reciprocal concessions.

Failing to slow Iran through diplomacy or sanctions should by now have taught a lesson to even the most credulous. With Mr. Kerry and Mr. Hagel poised to join the Obama administration, the temptation for the new arrivals to jump-start the stalled negotiations is distressingly clear. 

It is too late to get Mr. Kerry on the record before his appointment, but senators in the Hagel confirmation hearing should pin him down regarding his attitude toward a disastrous U-turn the West made last spring. That is when Western negotiators dropped their insistence that Iran halt all uranium enrichment, conceding instead that the regime could enrich to commercial,"reactor-grade" levels (approximately 4% of the U-235 isotope) if it stopped enriching to approximately 20%, purportedly to fuel a research reactor.

U.S. negotiators subsequently deluged the press with arguments that such a deal would be a major Western victory because 20% enrichment is far more dangerous than 4% enrichment, being much closer to the 90%+ level used in nuclear weapons. That sounds superficially plausible: 4% is arithmetically lower than 20%, and both are a long way from 90%.

Isn't it better to stop Iran from getting to 20%, the reasoning goes, even if it means conceding that they can enrich to 4%? No. Mr. Obama's negotiators are playing with numbers they don't really understand. Their crude physics is seriously flawed, based on a misunderstanding of the work required to enrich uranium to weapons-grade levels. As a result of the misreading, the negotiators' military-political conclusions are erroneous.

Here's the basic fact that puzzles us laymen, but not nuclear physicists: It takes much more work to enrich U-235 from its 0.7% concentration in natural uranium to reactor-grade levels (4% or 20%) than it takes to enrich from either of these levels to weapons-grade (90%+). Enrichment is simply the physical process of separating fissile U-235 isotopes from the unnecessary U-238 isotopes. Enriching 0.7% natural U-235 to 4% requires most of the work (70%) needed to enrich to levels over 90%. From 4%, enriching to 20% takes merely 15%-20% more of the work required to reach 90%+.

How can this be? To get from 0.7% to 4% U-235 concentration requires removing considerably more U-238 than doing the lesser amount of work to reach 20% and then 90%. Specifically, as an observer once described it: Natural uranium has 140 atoms of U-238 for every one of U-235. Enriching to 4% removes 115 of the U-238 atoms. Enriching to 20% means removing only 20 more U-238 atoms, and reaching 90% enrichment from there requires eliminating four-or-so more.

Accordingly, the amount of additional work required to increase either 4% or 20% enriched-uranium stockpiles to weapons-grade levels is of little consequence. The Non-Proliferation Education Center estimates the difference between the two reactor-grade levels to be only about three weeks of further enrichment for enough weapons-grade uranium for one nuclear device. As the Wisconsin Project on Nuclear Arms Control explains, "In either case, further enrichment to weapon-grade would take a matter of weeks or months, depending on the number of centrifuges devoted to the task."

In seeking a superficially reasonable deal, the West thus made a senseless concession by allowing enrichment even to 4%. Enrichment to any higher level will require mere baby steps to reach the Tehran regime's nuclear-arms destination. This problem cannot be solved by international inspections. Tehran would simply be too close to a "break-out" point that it could quickly achieve after expelling inspectors.

Once Iran is legitimized for enriching to reactor-grade levels-contrary to multiple Security Council resolutions requiring the cessation of all enrichment-related activities-any remaining possibility of stopping it from making nuclear weapons effectively disappears. Moreover, once "negotiations" recommence, the pressure on Israel not to strike militarily against Iran's nuclear program will swell yet again. And Iran will continue to chug steadily ahead with its ever-broader, deeper and more-threatening weapons plans.

Before the West makes one of its biggest mistakes in three decades of dealing with the ayatollahs, senators on Thursday must find out from Chuck Hagel where he stands.